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DUDLEY KNOX LIBRARY 
NAVAL PC3TGRADUATE SCHOOL 
MONTERFY. CALIFORNIA 93943 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




THESIS 


MODIFICATION OF HUFFMAN CODING 


by 


Suha Kilic; 


March 1985 


Thesis Advisor: R. W. Hamming 



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1. REPORT NUMBER 


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3. RECIPIENT'S CATALOG NUMBER 


4. TITLE (and Subtitle) 

Modification of Huffman Coding 


5. TYPE OF REPORT & PERIOD COVERED 

Master's Thesis 
March 1985 


S. PERFORMING ORG. REPORT NUMBER 


7. AUTHORC*; 

Suha Kilig 


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Naval Postgraduate School 
Monterey, California 93943 


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Naval Postgraduate School 
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March 1985 


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18. SUPPLEMENTARY NOTES 


19. KEY WORDS (Continue on reverse aide II necaeaary and Identity by block number) 

Huffman Coding, reduction of variance, increase in mean time 


20. ABSTRACT (Continue on reverse aide It necaaaary and Identity by block number^ 

Huffman Coding minimizes the average number of coding digits per 
message. Minimizing the mean time by this method raises the problem 
of large variance. When the variance is large there is a greater 
probability that an arbitrary encoded message significantly exceeds 
the average. The delicate point here is the danger of an urgent message 
taking more time than expected, in addition to larger bandwidth or 
buffer requirements. 



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20. 

With this research a large reduction of variance versus a small 
increase in mean time is examined for the purpose of modifying Huffman, 
Coding for a particular alphabet. 



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Approved for public release; distribution is unlimited. 

Modification of Huffman Coding 

by 

Suha Kilig 
Lt.Jg., Turkish Navy 
B.S., Turkish Naval Academy, 1978 

Submitted in partial fulfillment of the 
requirements for the degree of 

MASTER OF SCIENCE IN TELECOMMUNICATIONS SYSTEMS MANAGEMENT 

from the 

NAVAL POSTGRADUATE SCHOOL 
March 1985 



7Ar 



'f-T 






0^ , ^^ 



ABSTRACT 



Huffman Coding minimizes the average number of coding 
digits per message. Minimizing the mean time by this method 
raises the problem of large variance. When the variance is 
large there is a greater probability that an arbitrary 
encoded message significantly exceeds the average. The 
delicate point here is the danger of an urgent message 
taking more time than expected, in addition to larger band- 
width or buffer requirements. 

With this research a large reduction of variance versus 
a small increase in mean time is examined for the purpose of 
modifiying Huffman Coding for a particular alphabet. 



DhUi^tt.^ IxiiUX LIBRARY 

„: ••■-'T.-: SCHOOL 

'^^^ '^IFORNIA 95943 



TABLE OF CONTENTS 



I. THE INTRODUCTION 9 

A. HUFFMAN CODING 9 

B. VARIOUS CODES AND REDUCTION OF VARIANCE ... 12 

II. MODIFICATION OF HUFFMAN CODING FOR A 

PARTICULAR ALPHABET .14 

A. A PARTICULAR ALPHABET 14 

B. ASSIGNMENT OF THE CODES 14 

III. THE EVALUATION OF RESULTS 60 

APPENDIX A: THE MAGAZINE ARTICLES AND PROGRAMS 70 

A. THE MAGAZINE ARTICLES 70 

B. PROGRAMS 80 

APPENDIX B: THE LISP PROGRAM OF CODING PROCESS 8 3 

APPENDIX C: THE SAS POGRAM USED FOR FINDING THE 

BUFFER SIZE 8 6 

LIST OF REFERENCES 89 

INITIAL DISTRIBUTION LIST 90 



LIST OF TABLES 

1. Symbol Characteristics of the Particular 

Alphabet 17 

2. Symbol Probabilities in Decreasing Order 18 

3. Huffman Codes for the Particular Alphabet .... 19 

4. Various Codes for the Particular Alphabet .... 20 

5. Data for Figure 3.1 Through 3.3 63 

6. Maximum Buffer Length for Minimum Output Rate . . 66 

7. Maximum Buffer Length for Different Output 

Rates 69 



LIST OF FIGURES 

1.1 Step 1 of Huffman Coding 10 

1.2 Step 2 of Huffman Coding 10 

1.3 Step 3 of Huffman Coding 11 

1.4 Step 4 of Huffman Coding 11 

1.5 Final Code Words 11 

1.6 Various Codes 12 

1.7 Variance Versus Mean Time for Five Symbols .... 13 

2.1 Step 2 of Huffman Coding for N = 1 15 

2.2 Step 2 of Huffman Coding for E = . 13 16 

3.1 Variance - Mean Time Trade-off for the 

Particular Alphabet 61 

3.2 Lower Bound for Variance Reduction 62 

3 . 3 Sacrifice in Mean Time Versus Decrease in 

Variance 65 

3.4 Maximum Buffer Length Versus the Mean Time .... 67 



ACKNOWLEDGEMENTS 

The author wishes to extend deep gratitude and apprecia- 
tion to Prof. R. W. Hamming who suggested this area of 
research, and contributed time, expertise and constructive 
critism during the course of this work. 

Sincere thanks are due to Prof. Daniel R. Dolk, who, as 
second reader, has been instrumental in the criticism of 
this thesis . 

The author is also indebted to Prof. Bruce McLennan for 
the use of his program for Huffman Coding, and his modifica- 
tion of it to allow for different variable length codes. 

A special thanks is due to Applications Programmer 
Dennis R. Mar for training the author to use Statistical 
Analysis System (SAS) package programs. 



8 



I. THE INTRODUCTION 

In a digital transmission system, the requirement to 
maximize the data transfer rate drives the redundancy of the 
source toward a minimum. One way to reduce the redundancy 
of the source is to encode the source information with a 
variable length code such as a Huffman Code [Ref s . 1,2]. 
Such source code encoding assigns short bit sequences to 
source symbols with a high frequency of occurrence, and long 
bit sequences to source symbols with a low frequency of 
occurrence. The bandwith requirement is therefore dependent 
on the average code word lengths . 

A. HUFFMAN CODING 

Using only the probabilities of the various symbols 
being sent, Huffman Coding provides an organized technique 
for finding the code of minimum average length. The proce- 
dure is illustrated in the following example. 

Suppose that we wish to code five symbols, SI, S2, S3, 
S4, and S5 with the probabilities 0.125, 0.0625, 0.25, 
0.0625, and 0.5 respectively. The Huffman procedure can be 
accomplished in four steps . 

Step 1. Arrange the symbols in order of decreasing prob- 
ability. If there are equal probabilities, choose any of 
the various possibilities. See (Figure 1.1). 

Step 2. Combine the bottom two entries to form a new 
entry with a probability equal to the sum of the original 
probabilities. If necessary, reorder the list so that 
probabilities are still in descending order. See (Figure 
1.2). Note that the bottom entry in the right hand 
column is a combination of S2 and S4. 



Symbol 



Probability 



S5 
S3 
SI 
S2 
S4 



0.5 

0.25 

0.125 

0.0625 

0.0625 



Figure 1.1 Step 1 of Huffman Coding 



Symbol 


Prob. 


Prob. 


S5 


0.5 


0.5 


S3 


0.25 


0.25 


SI 


0.125 


0.125 


S2 


0.06251 ^ 


^0.125 


S4 


0.0625J 





Figure 1.2 Step 2 of Huffman Coding 

Step _3. Continue combining in pairs until only two 
entries remain. See (Figure 1.3). 

Step 4. Assign code words by starting at right with the 
most significant bit. Move to the left and assign 
another bit if a split occurred. The assigned bits are 
shown in parenthesis in Figure 1.4. 
Finally, the code words are given in Figure 1.5. 



10 



Symbol Prob . Prob . Prob . Prob . 

S5 0.5 0.5 0.5 0.5 

53 0.25 0.25 0.251 ^r . 5 

51 0.125 0. 125 1____-^ 0.25 1 

52 0.06251^^^^^^0.125 1 

54 0.06251 

Figure 1.3 Step 3 of Huffman Coding 

Symbol Prob. Prob. Prob. Prob. 

55 0.5 0.5 0.5 0.5 (0) 

53 0.25 0.25 0.25 (10)(^0.5 (1) 

51 0.125 0.125 (110)1^0.25 (11){ 

52 0.0625 (1110)1^^0.125 (111)( 

54 0.0625 (1111)1 

Figure 1.4 Step 4 of Huffman Coding 

SI 110 

S2 1110 

S3 10 

S4 1111 

S5 

Figure 1.5 Final Code Words 



11 



From Figure 1 . 5 we get code lengths (3, 4, 2, 4, 1), and 
the average the average length is given by 

L = 0.125(3) + 0.0625(4) + 0.25(2) + 0.0625(4) + 0.5(1) 

L = 1.875 

The Huffman code is the shortest possible code, but the 
variance is given by 

V = 0.125(3 - 1.875)2+ 0.0625(4 - 1.875)'+ 0.25(2 - 1.875)' 

+ 0.0625(4 - 1.875)' + 0.5(1 - 1.875)' = 1.109375 

By comparison, Block Coding, which assignes codes of 
equal length to each symbol, would have produced an average 
length of 3 with zero variance, 

B. VARIOUS CODES AND REDUCTION OF VARIANCE 

Figure 1.6 shows three different codes for the same 
source symbols used above. 



Symbol 



Prob. Code 1 (Huffman) Code 2 



Code 3 



55 


0.5 





S3 


0.25 


10 


SI 


0.125 


110 


S2 


0.0625 


1110 


S4 


0.0625 


1111 


Average length = 


1.875 


Variance 


= 


1.109375 






00 


100 


01 


101 


10' 


110 


110 


111 


111 


2 


2.125 


1 


0.109375 



Figure 1.6 Various Codes 



12 



The results of Figure 1.6 show that decreasing average 
length causes an increase in variance. A plot of the results 
is given in Figure 1.7. 




2.0 

MEAN TIME 



3.0 



Figure 1.7 Variance Versus Mean Time for Five Symbols 



13 



II. MODIFICATION OF HUFFMAN CODING FOR A PARTICULAR ALPHABET 

A. A PARTICULAR ALPHABET 

The intent of this research in the early stages was to 
find an efficient variable length code for a Turkish On-Line 
communication device. For security reasons, Turkish letter 
frequencies in military usage are not available. Therefore, 
common usage letter and symbol frequencies were determined 
using two articles from a popular Turkish science magazine 
[Ref s . 3,4]. The magazine articles, the Fortran language 
program and Statistical Analysis System (SAS) package 
program are given in Appendix A [Ref. 5]. The frequencies 
and other statistical characteristics obtained this way are 
given in Table 1. Table ?, contains the symbols re- arranged 
in order of decreasing frequency, along with their respec- 
tive probabilities of occurance. 

B. ASSIGNMENT OF THE CODES 

Using the derived frequency data, the symbols of this 
alphabet were to be assigned various codes, but there are 
many other codes to be examined for the purpose of reduction 
of variance versus increase in mean time. This process was 
too complex and time consuming to do manually for an 
alphabet of 47 symbols. For this reason the author used a 
program written in List Programming (LISP) language, shown 
in Appendix B [Ref s . 6,7]. This program is run with two 
parameters (N,E), to assign the code words to the symbols. 
These parameters serve the purpose of modifying the Huffman 
Coding process to obtain lower variance codes. Both parame- 
ters are based on the idea of shifting the combined entries 
higher than their positions in the Huffman Coding process. 



14 



Practically this assignment is expected to result in lower 
variance codes. [Ref. 1: p. 68]. The definitions of the 
parameters are given below. 

(1) N is defined as the number of relative places a 
combined entry is moved, after positioning it in 
order of decreasing probability. If N is set to 
0, we obtain Huffman coding, if N is set to 1, 
combined entries are moved one position higher 
than their position in the Huffman coding 
process. Setting N to 1, step 2 of the Huffman 
Coding process for the example given in the 
previous chapter can be modified as shown in 
Figure 2.1. 




Symbol Prob . Prob . 



S5 
S3 
SI 
S2 
S4 



Figure 2.1 Step 2 of Huffman Coding for N = 1 

(2) The second parameter E, is a constant which is 
added to the probability sum of each combined 
entry when generating a code. This causes the 
combined entry to appear higher in the 
decreasing probability list (recall step 2 of 
the Huffman coding process described in the 
previous chapter), which results in a lower 
variance code. Like N, if is assigned to E, 
the Huffman code will result. Setting E to 



15 



0.13, step 2 of Huffman Coding process for the 
example given in the previous chapter can be 
modified as shown in Figure 2.2. We do not need 
to worry that the sum of all the probabilities 
is no longer equal to one. 



Symbol 


Prob. 


Prob. 


S5 


0.5 


0.5 


S3 


0.25 


0.255 


SI 


0.125 


y^ 0.25 


S2 


0.06251 / 


0.125 


S4 


0.06251 





Figure 2.2 Step 2 of Huffman Coding for E = 0.13 

The Huffman code, which is obtained by setting N and E 
to 0, is given in Table 3. This table also includes the 
entropy of this particular alphabet. The entropy gives a 
lower bound on the amount of compression that can be 
achieved by any encoding using only the single letter 
frequencies, as done here. [Ref. 1: pp.104 -108]. The 
other codes, obtained with different N and E values, are 
given in Tables 4.1 through 4.40. These tables also include 
the average length and the variance of their respective code 
words . 



16 







TABLE 1 






Symbol 


Characteristics of the 


Particular 


Alphabet 


SYMBOL 


FREQUENCY 


CUM FREQ 


PERCENT 


CUM PERCENT 


• 


182 


182 


1.017 


1.017 


s 


12 


194 


0.067 


1.084 


15 


209 


0.084 


1.168 


• 
• 


11 


220 


0.061 


1.229 




3 


223 


0.017 


1.246 


space 


2387 


2610 


13.339 


14.585 


• 


219 


2829 


1.224 


15.809 


■ 


1 


2830 


0.006 


15.814 


• 
• 


6 


2836 


0.034 


15.848 


1 


29 


2865 


0.162 


16.010 


tf 


20 


2885 


0.112 


16.122 


A 


1687 


4572 


9.427 


25.549 


B 


337 


4909 


1.883 


27.432 


C 


293 


5202 


1.637 


29.070 


D 


628 


5830 


3.509 


32.579 


E 


1423 


7253 


7.952 


40.531 


F 


64 


7317 


0.358 


40.889 


G 


391 


7708 


2.185 


43.073 


H 


104 


7812 


0.581 


43.655 


I 


1884 


9696 


10.528 


54.183 


J 


8 


9704 


0.045 


54.227 


K 


691 


10395 


3.861 


58.089 


L 


918 


11313 


5.130 


63.219 


M 


527 


11840 


2.945 


66.164 


N 


1183 


13023 


6.611 


72.775 





476 


13499 


2.660 


75.434 


P 


123 


13622 


0.687 


76.122 


R 


1089 


14711 


6.085 


82.207 


S 


713 


15424 


3.984 


86.192 


T 


575 


15999 


3.213 


89.405 


U 


924 


16923 


5.163 


94.568 


V 


156 


17079 


0.872 


95.440 


W 


7 


17086 


0.039 


95.479 


X 


1 


17087 


0.006 


95.485 


Y 


480 


17567 


2.682 


98. 167 


Z 


177 


17744 


0.989 


99.156 





35 


17779 


0.196 


99.352 


1 


24 


17803 


0.134 


99.486 


2 


16 


17819 


0.089 


99.575 


3 


13 


17832 


0.073 


99.648 


4 


12 


17844 


0.067 


99.715 


5 


15 


17859 


0.084 


99.799 


6 


8 


17867 


0.045 


99.844 


7 


5 


17872 


0.028 


99.871 


8 


13 


17885 


0.073 


99.944 


9 


10 


17895 


0.056 


100.000 



17 



TABLE 2 
Symbol Probabilities in Decreasing Order 



SYMBOL 


PROBABILITY 


space 


0.13339 


I 


0.10528 


A 


0.09427 


E 


0.07952 


N 


0.06611 


R 


0.06085 


U 


0.05163 


L 


0.05130 


S 


0.03984 


K 


0.03861 


D 


0.03509 


T 


0.03213 


M 


0.02945 


Y 


0.02682 





0.02660 


G 


0.02185 


B 


0.01883 


C 


0.01637 


9 


0.01224 


■ 


0.01017 


Z 


0.00989 


V 


0.00872 


P 


0.00687 


H 


0.00581 



SYMBOL 


PROBABILITY 


F 


0.00358 





0.00196 


f 


0.00162 


1 


0.00134 


t? 


0.00112 


2 


0.00089 


) 


0.00084 


5 


0.00084 


3 


0.00073 


8 


0.00073 


( 


0.00067 


4 


0.00067 


9 


0.00061 


9 


0.00056 


J 


0.00045 


6 


0.00045 


W 


0.00039 


• 
• 


0.00034 


7 


0.00028 


- 


0.00017 


? 


0.00006 


X 


0.00006 





0.00000 



18 







TABLE 3 








Huffman Codes 


for the Particul 


ar Alphabet 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


010 


1 




100101101 


I 


101 


1 




0000011100 


A 


111 


M 




0000011111 


E 


0001 


2 




1001001011 


N 


0110 


) 




1001011001 


R 


1000 


5 




1001011000 


U 


1100 


3 




1001011110 


L 


1101 


8 




1001011101 


S 


00100 


( 




1001011111 


K 


00101 


4 




00000111010 


D 


00111 


• 

> 




00000111011 


T 


OHIO 


9 




00000111101 


M 


01111 


J 




10010010101 


Y 


10011 


6 




10010010100 





000000 


W 




10010111000 


G 


000010 


• 
• 




10010111001 


B 


001100 


7 




000001111001 


C 


001101 


- 




0000011110000 


» 


0000010 


? 

• 




00000111100011 


• 


0000110 


X 




000001111000100 


Z 


0000111 


Q 




000001111000101 


V 


1001000 








p 


1001010 


Entrc 


py 


(H) = 4.27876 


H 


00000110 


Mean 


Time (L) = 4.30771 


F 


10010011 


Variance 


(V) - 1.91828 





100100100 









19 







TABLE 4 


.1 




V 


arious Codes 


for the Particular Alphabet 


SYMBOL 


CODE WORDS 


< 


SYMBOL 


CODE WORDS 


space 


100 




f 


011010001 


I 


110 




1 


101000100 


A 


0000 




»f 


001010010 


E 


0011 




2 


001010011 


N 


0111 




) 


0110100110 


R 


0101 




5 


0110100000 


U 


1110 




3 


0110100111 


L 


1011 




8 


0110100100 


S 


00100 




( 


1010001110 


K 


00010 




4 


0110100101 


D 


00011 




• 


1010001100 


T 


01100 




9 


1010001101 


M 


01000 




J 


1010001011 


Y 


01001 




6 


1010001010 





10101 




W 


01101000011 


G 


11111 




• 
• 


10100011110 


B 


001011 




7 


011010000100 


C 


011011 




- 


101000111110 


J 


101001 




? 


101000111111 


. 


111100 




X 


0110100001010 


Z 


111101 




Q 


0110100001011 


V 


0010101 








p 


0110101 


N 


= 1 , E 


= 0.0 ; 


H 


00101000 


M 


san Time 


(L) = 4.31277 


F 


10100000 


V 


ariance 


(V) - 1.41646 





10100001 


C 


ode No = 


1 



20 







Table 4.2 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


101 


1 




001010011 


I 


110 


1 




001010001 


A 


0011 


ff 




111011100 


E 


0101 


2 




100100010 


N 


0110 


) 




111011000 


R 


0111 


5 




100100011 


U 


1000 


3 




111011111 


L 


1111 


8 




111011001 


S 


00010 


( 




100100001 


K 


00011 


4 




100100000 


D 


00000 


• 
> 




0010100100 


T 


00001 


9 




0010100101 


M 


01000 


J 




1110111011 


Y 


01001 


6 




0010100000 





10011 


W 




0010100001 


G 


001011 


• 




1110111100 


B 


001000 


7 




1110111101 


C 


001001 


- 




111011101000 


) 


111010 


? 

• 




111011101010 


• 


111000 


X 




111011101001 


Z 


111001 


Q 




111011101011 


V 


0010101 








p 


1001001 


N = 3 


, E 


= 0.0 ; 


H 


1001010 


Mean 


Time 


(L) = 4.3194 


F 


1001011 


Variance 


(V) 3 1.34446 





11101101 


Code 


No = 


2 



21 



Table 4.3 
Various Codes for the Particular Alphabet (cont'd.) 



SYMBOL CODE WORDS 
space 101 



I 


0010 


A 


0011 


E 


0101 


N 


0111 


R 


1001 


U 


1111 


L 


1100 


S 


00010 


K 


00011 


D 


00000 


T 


00001 


M 


01000 


Y 


01001 





11100 


G 


01100 


B 


01101 


C 


100011 


J 


100000 


• 


100001 


z 


111011 


V 


110110 


p 


110111 


H 


1101000 


F 


11010110 





10001011 



SYMBOL CODE WORDS 
10001000 

1 10001001 
11010010 

2 11010011 
) 11101010 

5 11101001 

3 11101000 

8 110101000 
( 110101110 

4 110101011 
; 110101111 

9 100010100 
J 100010101 

6 111010110 
W 111010111 

: 1101010010 

7 1101010101 
11010100110 

? 11010101000 . 
X 11010100111 
Q 11010101001 

N = 4 , E = 0.0 ; 
Mean Time (L) = 4.36186 
Variance (V) = 0.93749 
Code No = 3 



22 







Table 4.4 




Various 


Codes for the 


i Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


0001 


1 


11110101 


I 


0010 


1 


11101110 


A 


0011 


ff 


11110110 


E 


1010 


2 


11101111 


N 


0110 


) 


11110111 


R 


1001 


5 


11101010 


U 


0100 


3 


11101011 


L 


0101 


8 


100000010 


S 


1100 


( 


100000110 


K 


1101 


4 


100000011 


D 


00000 


> 
9 


100000111 


T 


00001 


9 


100000100 


M 


OHIO 


J 


111011000 


Y 


11111 


6 


100000101 





11100 


W 


111011001 


G 


10110 


• 
• 


1000000000 


B 


10111 


7 


1000000001 


C 


100001 


- 


10000000100 


J 


111100 


• 


10000000110 


. 


011110 


X 


10000000101 


Z 


011111 


Q 


10000000111 


V 


100010 






p 


100011 


N = 4 , E 


= 0.00100 ; 


H 


1110100 


Mean Time 


(L) = 4.4168 


F 


11101101 


Variance 


(V) = 0.68287 





11110100 


Code No = 


4 



23 







Table 


4.5 






Various 


Codes for the Part 


icular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 




SYMBOL 


CODE WORDS 


space 


0000 




f 




1010011 


I 


0001 




1 




01111000 


A 


0110 




If 




01111001 


E 


1000 




2 




01111011 


N 


1001 




) 




01001001 


R 


1011 




5 




01111110 


U 


1110 




3 




01111111 


L 


1111 




8 




01001010 


S 


00100 




( 




01111100 


K 


00101 




4 




01001011 


D 


01010 




• 
5 




11011010 


T 


OHIO 




9 




01111101 


M 


11000 




J 




11011000 


Y 


01000 




6 




11011001 





11010 




W 




011110101 


G 


10101 




• 




010010000 


B 


00110 




7 




010010001 


C 


00111 




- 




110110110 


) 


010011 








110110111 


• 


010110 




X 




0111101000 


Z 


010111 




Q 




0111101001 


V 


110111 










p 


101000 




N = 8 


, E 


- 0.0 ; 


H 


110010 




Mean 


Time 


(L) = 4.45705 


F 


110011 




Variance 


(V) = 0.52959 





1010010 




Code 


No = 


5 



24 







Table 4.6 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


0110 


f 


1111011 


I 


0111 


1 


1111000 


A 


1110 


It 


1111110 


E 


1011 


2 


1111001 


N 


1100 


) 


1111111 


R 


1001 


5 


1111100 


U 


01011 


3 


1111101 


L 


00000 


8 


0101000 


S 


00001 


( 


0101001 


K 


00100 


4 


00010010 


D 


00101 


■ 

> 


00010011 


T 


00110 


9 


00010000 


M 


00111 


J 


00010001 


Y 


01000 


6 


01010100 





01001 


W 


01010101 


G 


10100 


• 
• 


00010110 


B 


10101 


7 


00010111 


C 


11010 


- 


00010100 


) 


11011 


? 


00010101 


• 


000110 


X 


01010110 


Z 


000111 


Q 


01010111 


V 


100000 






P 


100001 


N = 7 , E 


- 0.01000 ; 


H 


100010 


Mean Time 


(L) = 4.53922 


F 


100011 


Variance 


(V) = 0.45146 





1111010 


Code No = 


6 



25 



SYMBOL 


CODE WORDS 


space 


0101 


I 


0111 


A 


1011 


E 


1000 


N 


1110 


R 


00111 


U 


00000 


L 


00001 


s 


00010 


K 


00011 


D 


00100 


T 


00101 


M 


11110 


Y 


01000 





01001 


G 


01100 


B 


01101 


C 


11010 


J 


11011 


• 


10010 


Z 


10011 


V 


111110 


p 


mill 


H 


1100100 


F 


1100101 





1100000 



Table 4.7 








i Particular 


Alphabet (cont'd. 


) 


SYMBOL 


CODE WORDS 




» 




1100001 




1 




1100010 




fi 




1100110 




2 




1100011 




) 




1100111 




5 




1010010 




3 




1010011 




8 




1010000 




( 




1010001 




4 




1010110 




• 

> 




1010111 




9 




1010100 




J 




1010101 




6 




00110100 





w 



7 

X 

Q 



00110101 
00110110 
00110111 
00110000 
00110001 
00110010 
00110011 



N = 9 , E = 0.00750 ; 
Mean Time (L) = 4.58711 
Variance (V) = 0.42911 
Code No = 7 



26 







Table 4.8 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1011 


f 




111001 


I 


1111 


1 




0000010 


A 


1100 


»f 




0000011 


E 


1101 


2 




0101110 


N 


01010 


) 




0101111 


R 


01101 


5 




0101100 


U 


OHIO 


3 




0101101 


L 


00010 


8 




0111100 


S 


00011 


( 




0111101 


K 


00100 


4 




0110010 


D 


00101 


* 




0110011 


T 


00110 


9 




0110000 


M 


00111 


J 




0110001 


Y 


01000 


6 




0000000 





01001 


W 




0000001 


G 


10000 


• 
• 




0000110 


B 


10001 


7 




0000111 


C 


10010 


- 




0000100 


9 


10011 


• 




0000101 


• 


101000 


X 




0111110 


Z 


101001 


Q 




0111111 


V 


101010 








P 


101011 


N = 11 , 


E = 0.01000 ; 


H 


111010 


Mean 


Time 


; (L) = 4.65856 


F 


111011 


Variance 


(V) = 0.38929 





111000 


Code 


No = 


8 



27 



SYMBOL 


CODE WORDS 


space 


1010 


I 


1011 


A 


1100 


E 


00000 


N 


00001 


R 


00010 


U 


01000 


L 


00100 


S 


00101 


K 


00110 


D 


00111 


T 


11100 


M 


01101 


Y 


01010 





01011 


G 


10000 


B 


10001 


C 


10010 


i 


10011 


• 


110100 


Z 


110101 


V 


011000 


p 


110110 


H 


011001 


F 


110111 





111110 



Table 4.9 








e Particular 


Alphabet (cont'd. 


) 


SYMBOL 


CODE WORDS 




t 




mill 




1 




111100 




n 




111101 




2 




111010 




) 




111011 




5 




0001100 




3 




0001101 




8 




0100100 




( 




0100101 




4 




0111000 




• 
5 




0111001 




9 




0111010 




J 




0111011 




6 




0111110 




W 




0111111 




• 
• 




0111100 




7 




0111101 




- 




0100110 




• 




0100111 





X 0001110 
Q 0001111 

N = 13 , E = 0.00250 ; 
Mean Time (L) = 4.73389 
Variance (V) = 0.34297 
Code No = 9 



28 







Table 4.10 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1001 


» 


110001 


I 


1011 


1 


101010 


A 


00000 


1? 


101011 


E 


00001 


2 


101000 


N 


00010 


) 


101001 


R 


00011 


5 


110110 


U 


00100 


3 


110111 

• 


L 


00101 


8 


011000 


S 


11110 


( 


011001 


K 


11010 


4 


0011000 


D 


01101 


• 
9 


0011001 


T 


01000 


9 


1111100 


M 


01001 


J 


1111101 


Y 


01010 


6 


1111110 





01011 


W 


1111111 


G 


OHIO 


■ 
• 


0011010 


B 


01111 


7 


0011110 


C 


10000 


- 


0011011 


J 


10001 


7 

■ 


0011111 


• 


110010 


X 


0011100 


z 


110011 


Q 


0011101 


V 


111000 






p 


111001 


N = 10 , 


E = 0.01000 ; 


H 


111010 


Mean Time 


t (L) = 4.82519 


F 


111011 


Variance 


(V) = 0.28005 





110000 


Code No = 


10 



29 







Table 4.11 






Various 


Codes for the 


i Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1101 


! 




111011 


I 


00010 


1 




111000 


A 


00011 


tf 




111001 


E 


00100 


2 




101100 


N 


00101 


) 




101110 


R 


00110 


5 




101101 


U 


00111 


3 




111100 

• 


L 


01000 


8 




101111 


S 


01001 


( 




111101 


K 


01010 


4 




100010 


D 


01011 


« 




100011 


T 


01100 


9 




100100 


M 


01101 


J 




100101 


Y 


OHIO 


6 




0000010 





01111 


W 




0000011 


G 


10100 


• 
• 




0000000 


B 


10101 


7 




0000001 


C 


11000 


- 




0000110 


J 


11001 


9 




0000111 


• 


100000 


X 




0000100 


Z 


100001 


Q 




0000101 


V 


100110 








p 


100111 


N = 8 


, E 


= 0.02500 ; 


H 


111110 


Mean 


Time 


(L) = 4.92818 


F 


111111 


Variance 


(V) = 0.19330 





111010 


Code 


No = 


11 



30 







Table 4.12 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS • 


space 


00000 


T 




011011 


I 


00001 


1 




011100 


A 


00011 


»f 




011101 


E 


00101 


2 




011110 


N 


00111 


) 




100000 


R 


01000 


5 




011111 


U 


01001 


3 




100001 


L 


01011 


8 




011000 


S 


10100 


( 




100010 


K 


10101 


4 




011001 


D 


10110 


9 




100011 


T 


10111 


9 




100100 


M 


11100 


J 




100110 


Y 


11000 


6 




100101 





11001 


W 




100111 


G 


11010 


• 
• 




111010 


B 


11011 


7 




111011 


C 


11110 


- 




0011000 


9 


11111 


? 




0011010 


■ 


000100 


X 




0011001 


Z 


000101 


Q 




0011011 


V 


001000 








P 


001001 


N = 25 , 


E = 0.0 ; 


H 


010100 


Mean 


Time 


(L) = 5.06011 


F 


010101 


Variance 


(V) - 0.05707 





011010 


Code 


No = 


12 



31 



Table 4. 13 
Various Codes for the Particular Alphabet (cont'd.) 



SYMBOL CODE WORDS 
space Oil 



I 

A 
E 
N 
R 
U 
L 
S 
K 
D 
T 
M 
Y 

G 
B 
C 



Z 

V 
P 
H 
F 




101 

111 

0010 

0101 

1001 

1101 

00000 

00010 

00011 

01000 

01001 

10000 

10001 

11000 

001100 

001110 

001111 

0000100 

0000110 

0000111 

1100100 

1100111 

00110111 

11001100 

11001101 



SYMBOL CODE WORDS 
001101001 

1 001101010 
001101011 

2 110010110 
) 110010111 

5 001101100 

3 001101101 

8 0000101000 
( 0000101010 

4 0000101001 
; 0000101100 

9 0000101011 
J 0000101101 

6 0000101110 
W 0000101111 
: 1100101000 

7 1100101001 
1100101010 

? 1100101011 

X 0011010000 

Q 0011010001 

N = , E = 0.00500 ; 
Mean Time (L) ^ 4.31961 
Variance (V) = 1.73177 
Code No = 13 



32 







Table 4. 14 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


101 


1 


011110001 


I 


110 


1 


011110010 


A 


0011 


»t 


011110011 


E 


0100 


2 


011110110 


N 


0101 


) 


011110111 


R 


1000 


5 


011110100 


U 


1001 


3 


011110101 


L 


1110 


8 


000000000 


S 


1111 


( 


000000001 


K 


00010 


4 


0000001010 


D 


00011 


• 

> 


0000001011 


T 


00100 


9 


0000001000 


M 


00101 


J 


0000001001 


Y 


01100 


6 


0000001110 





01101 


W 


0000001111 


G 


000001 


• 


0000001100 


B 


011111 


7 


0000001101 


C 


011100 


- 


0000111010 


5 


011101 


• 


0000111011 


• 


0000100 


X 


0000111000 


Z 


0000101 


Q 


0000111001 


V 


00001111 






p 


00000001 


N = 3 , E 


= 0.00250 ; 


H 


00001100 


Mean Time 


(L) = 4.32665 


F 


00001101 


Variance 


(V) = 1.59198 





011110000 


Code No = 


14 



33 



Table 4.15 
Various Codes for the Particular Alphabet (cont'd.) 

SYMBOL CODE WORDS 
01001001 

1 000011100 
000011101 

2 000011110 
) 000011111 

5 100101000 

3 100101010 

8 100101001 
( 100101011 

4 100101100 
; 100101101 

9 100101110 
J 100101111 

6 0000110000 
W 0000110010 
: 0000110001 

7 0000110100 
0000110011 

? 0000110110 
X 0000110101 
Q 0000110111 

N = , E = 0.01250 ; 
Mean Time (L) = 4.33631 
Variance (V) = 1.23500 
Code No = 15 



SYMBOL 


CODE WORDS 


space 


Oil 


I 


110 


A 


0001 


E 


0011 


N 


0101 


R 


1010 


U 


.1111 


L 


00000 


S 


00100 


K 


00101 


D 


01000 


T 


10001 


M 


10011 


Y 


10111 





11100 


G 


11101 


B 


000010 


C 


100100 


) 


100000 


• 


100001 


z 


101100 


V 


101101 


p 


0100101 


H 


0100110 


F 


0100111 





01001000 



34 







Table 4.16 






Various 


Codes for 


the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


101 


f 




1001111 


I 


111 


1 




00010000 


A 


0010 


ff 




00010001 


E 


0100 


2 




10000110 


N 


0101 


) 




10000111 


R 


0110 


5 




001101110 


U 


0111 


3 




001101111 


L 


1101 


8 




001101100 


S 


00000 


( 




001101101 


K 


00001 


4 




000110010 


D 


00111 


• 




000110011 


T 


10010 


9 




000110000 


M 


10001 


J 




000110001 


Y 


11000 


6 




0011010010 





000111 


W 




0011010011 


G 


000101 


• 
■ 




0011010000 


B 


001100 


7 




0011010001 


C 


100110 


- 




0011010110 


> 


110010 


? 

■ 




0011010111 


• 


110011 


X 




0011010100 


Z 


0001101 


Q 




0011010101 


V 


0001001 








p 


1000010 


N = 1 


, E 


= 0.00750 ; 


H 


1000000 


Mean 


Time 


(L) = 4.3443 


F 


1000001 


Variance 


(V) = 1.35389 





1001110 


Code 


No = 


16 



35 



Table 4.17 
Various Codes for the Particular Alphabet (cont'd.) 

SYMBOL CODE WORDS 
0111101 

1 1100000 
1100001 

2 01101100 
) 01101110 

5 01101101 

3 01101111 

8 000001100 
( 000001101 

4 000001110 
; 000001111 

9 0000010010 
J 0000010011 

6 0000010100 
W 0000010110 
: 0000010101 

7 0000010111 
00000100000 

? 00000100001 
X 00000100010 
Q 00000100011 

N = , E = 0.01500 ; 
Mean Time (L) = 4.36739 
Variance (V) = 1.24489 
Code No = 17 



SYMBOL 


CODE WORDS 


space 


010 


I 


111 


A 


0001 


E 


0011 


N 


1001 


R 


1010 


U 


1101 


L 


00001 


S 


00101 


K 


01100 


D 


OHIO 


T 


10001 


M 


10111 


Y 


11001 





000000 


G 


001001 


B 


011010 


C 


011111 


> 


110001 


• 


100000 


Z 


100001 


V 


101100 


p 


101101 


H 


0010000 


F 


0010001 





0111100 



36 



Table 4. 18 
Various Codes for the Particular Alphabet (cont'd.) 



SYMBOL CODE WORDS 

space 111 

I 0001 

A 0011 

E 0100 

N 0101 

R 1010 

U 0110 

L 0111 

S 00001 

K 10000 

D 11001 

T 00100 

M 00101 

Y 10010 
10011 
G 10110 
B 10111 
C 000000 

100010 

110100 

Z 110101 

V 1101100 
P 1101101 
H 1101110 
F 1101111 
1000110 



SYMBOL CODE WORDS 
1000111 

1 00000100 
00000101 

2 00000110 
) 00000111 

5 110001010 

3 110001011 

8 110001000 
( 110001001 

4 110001110 
; 110001111 

9 110001100 
J 110001101 

6 110000010 
W 110000011 
: 110000000 

7 IIOCOOIIO 
110000001 

? 110000111 

X 110000100 

Q 110000101 

N = 3 , E = 0.01000 ; 
Mean Time (L) = 4.37066 
Variance (V) = 0.95923 
Code No = 18 



37 



Table 4. 19 
Various Codes for the Particular Alphabet (cont'd.) 

SYMBOL CODE WORDS 
01110001 

1 01110010 
01110011 

2 00011010 
) 00011011 

5 00011000 

3 00011001 

8 00000100 
( 00000101 

4 01110110 
; 01110111 

9 010011010 
J 010011011 

6 010011000 
W 010011100 
: 010011001 

7 010011101 
0100111100 

? 0100111110 
X 0100111101 
Q 0100111111 

N = 6 , E = 0.00100 ; 
Mean Time (L) = 4.37112 
Variance (V) = 1.03108 
Code No = 19 



SYMBOL 


CODE WORDS 


space 


111 


I 


0101 


A 


0110 


E 


1000 


N 


1001 


R 


1010 


U 


1011 


L 


1100 


S 


1101 


K 


00101 


D 


00001 


T 


01000 


M 


00010 


Y 


00111 





01111 


G 


000000 


B 


000111 


C 


001000 


) 


001001 


• 


001100 


Z 


001101 


V 


0111010 


p 


0000011 


H 


0100100 


F 


0100101 





01110000 



38 





Table 4.20 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


Oil 


1 




1010101 


I 


111 


1 




10001100 


A 


0001 


ff 




10001101 


E 


0011 


2 




10001110 


N 


0100 


) 




10001111 


R 


0101 


5 




000001000 


U 


1100 


3 




000001001 


L 


1101 


8 




000001010 


S 


10100 


( 




000001011 


K 


10110 


4 




000001100 


D 


00100 


■ 
9 




000001110 


T 


00101 


9 




000001101 


M 


000000 


J 




100001000 


Y 


000011 


6 




000001111 





100000 


W 




100001010 


G 


100010 


• 
• 




100001001 


B 


101011 


7 




100001011 


C 


100100 


- 




100001100 


J 


100101 


• 




100001110 


• 


100110 


X 




100001101 


Z 


100111 


Q 




100001111 


V 


101110 








p 


101111 


N = 


, E 


= 0.02000 ; 


H 


0000100 


Mean 


Time 


(L) = 4.37334 


F 


0000101 


Variance 


(V) = 1.35521 





1010100 


Code 


No = 


20 



39 



Table 4.21 
Various Codes for the Particular Alphabet (cont'd.) 



SYMBOL 


CODE WORDS 


space 


111 


I 


0011 


A 


0100 


E 


1000 


N 


1011 


R 


1100 


U 


1101 


L 


00000 


S 


01111 


K 


01101 


D 


00010 


T 


00011 


M 


10101 


Y 


01010 





01011 


G 


10010 


B 


10011 


C 


001001 


» 


000010 


. 


011100 


Z 


011101 


V 


011000 


p 


011001 


H 


101000 


F 


101001 





0000110 



SYMBOL 



2 

) 
5 
3 
8 

( 
4 

« 

9 
J 
6 
W 



X 

Q 



CODE WORDS 
0000111 
00100010 
00100011 
00100000 
00100001 
001011110 
001011111 
001011010 
001011011 
001011000 
001011100 
001011001 
001011101 
001010010 
001010011 
001010000 
001010001 
001010110 
001010111 
001010100 
001010101 



N = 4 , E = 0.01250 ; 
Mean Time (L) = 4.39698 
Variance (V) = 0.86542 
Code No = 21 



40 







Table 4 


.22 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


< 


SYMBOL 


CODE WORDS 


space 


111 




f 


0111101 


I 


0110 




1 


10000010 


A 


1001 




f» 


10000011 


E 


1010 




2 


00000100 


N 


1011 




) 


00000101 


R 


1100 




5 


10000000 


• U 


1101 




3 


10000110 


L 


00010 




8 


10000001 


S 


00001 




( 


10000111 


K 


01000 




4 


10000100 


D 


00101 




9 


10000101 


T 


00111 




9 


00000110 


M 


10001 




J 


01001010 


Y 


OHIO 




6 


00000111 





01010 




W 


01001011 


G 


01011 




* 


01001000 


B 


000000 




7 


01001001 


C 


000110 




- 


01001110 


i 


000111 




7 

■ 


01001111 


• 


001000 




X 


01001100 


z 


001001 




Q 


01001101 


V 


001100 








p 


001101 


N 


= 8 , E 


= 0.00250 ; 


H 


0111110 


M( 


san Time 


(L) = 4.41819 


F 


0111111 


V. 


ariance 


(V) = 0.88848 





0111100 


C 


Dde No = 


22 



41 



Table 4.23 
Various Codes for the Particular Alphabet (cont'd.) 



SYMBOL CODE WORDS 
space 0000 



I 

A 
E 
N 
R 
U 
L 
S 
K 
D 
T 
M 
Y 

G 
B 
C 



Z 
V 
P 
H 
F 




0001 

0010 

0011 

0101 

0110 

0111 

1100 

1101 

1110 

10011 

10100 

10000 

01000 

10111 

11110 

100010 

010011 

101010 

101011 

101100 

101101 

1001010 

1001011 

10010010 

10001100 



SYMBOL CODE WORDS 
10001101 

1 11111010 
11111011 

2 11111000 
) 11111110 

5 11111001 

3 11111111 

8 10001110 
( 11111100 

4 10001111 
; 11111101 

9 01001010 
J 01001011 

6 01001000 
W 01001001 

: 100100010 

7 100100011 
100100000 

? 100100001 

X 100100110 

Q 100100111 

N = 4 , E = 0.00250 ; 
Mean Time (L) = 4.43677 
Variance (V) = 0.70212 
Code No = 23 



42 







Table 4.24 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


0100 


» 


0000111 


I 


0101 


1 


01101110 


A 


0111 


tf 


01101111 


E 


1000 


2 


01101010 


N 


1100 


) 


01101011 


R 


1010 


5 


01101000 


U 


1011 


3 

• 


01101001 


L 


1110 


8 


01101100 


S 


1111 


( 


01101101 


K 


00000 


4 


01100010 


D 


00010 


■ 


01100011 


T 


00011 


9 


01100000 


M 


10010 


J 


01100001 


Y 


10011 


6 


01100110 





11010 


W 


01100111 


G 


11011 


• 
• 


01100100 


B 


001101 


7 


01100101 


C 


000010 


- 


01110010 


J 


001011 


9 

m 


00110011 


• 


001000 


X 


00110000 


Z 


001001 


Q 


00110001 


V 


001110 






p 


001111 


N = 4 , E 


= 0.02000 ; 


H 


0010100 


Mean Time 


(L) = 4.46044 


F 


0010101 


Variance 


(V) = 0.62683 





0000110 


Code No = 


24 



43 







Table 4.25 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


0110 


t 




1100110 


I 


0111 


1 




1001010 


A 


1000 


Tl 




1001011 


E 


1010 


2 




1100000 


N 


1011 


) 




1100001 


R 


1101 


5 




0000100 


U 


1110 


3 

• 




0000101 


L 


00000 


8 




01000100 


S 


00010 


( 




01000110 


K 


00011 


4 




01000101 


D 


00100 


• 
> 




01000111 


T 


00101 


9 




01000000 


M 


10011 


J 




01000001 


Y 


00110 


6 




01000010 





00111 


W 




01000011 


6 


01010 


• 
• 




11001110 


B 


01011 


7 




11001111 


C 


11110 


- 




100100000 


9 


11111 


• 




100100010 


• 


110001 


X 




100100001 


Z 


000011 


Q 




100100011 


V 


010010 








p 


010011 


N = 11 , 


E = 0.0 ; 


H 


1001001 


Mean 


Time 


i (L) - 4.49867 


F 


1100100 


Variance 


(V) = 0.50127 





1100101 


Code 


No = 


25 



44 







Table 4 


.26 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


< 


BYMBOL 


CODE WORDS 


space 


0101 




1 




1011111 


I 


0110 




1 




0001000 


A 


0111 




ft 




0001001 


E 


1001 




2 




0001110 


N 


1010 




) 




0001111 


R 


1100 




5 




00111000 


U 


1101 




3 




00111001 


L 


00100 




8 




00111010 


S 


00101 




( 




00111011 


K 


01000 




4 




00111110 


D 


01001 




• 




00111111 


T 


11100 




9 




00111100 


M 


11101 




J 




00111101 


Y 


10000 




6 




00110010 





10001 




W 




00110011 


G 


11110 




• 
• 




00110000 


B 


11111 




7 




00110001 


C 


000110 




- 




00110110 


9 


000101 




• 




00110111 


■ 


000000 




X 




00110100 


Z 


000001 




Q 




00110101 


V 


000010 










P 


000011 


N 


= 5 


, E 


= 0.02500 ; 


H 


101100 


Mf 


san 


Time 


(L) = 4.51559 


F 


101101 


V, 


ariance 


(V) = 0.51347 





101110 


C< 


Dde 


No = 


26 



45 







Table 4.27 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


0101 


f 


0111011 


I 


1000 


1 


0100110 


A 


1010 


rf 


0100111 


E 


1100 


2 


0110110 


N 


1101 


) 


0110111 


R 


1111 


5 


0110100 


U 


00011 


3 


0111000 


L 


01000 


8 


0110101 


S 


01111 


( 


1011000 


K 


01100 


4 


0111001 


D 


10111 


■ 


1011001 


T 


00100 


9 


1011010 


M 


00101 


J 


1011011 


Y 


00110 


6 


0001000 





00111 


W 


0001001 


G 


10010 


• 
• 


01001010 


B 


10011 


7 


01001011 


C 


11100 


- 


000000000 


S 


11101 


? 


000000010 


• 


000001 


X 


000000001 


z 


000101 


Q 


000000011 


V 


000010 






p 


000011 


N = 13 , 


E = 0.0 ; 


H 


0000001 


Mean Time 


; (L) = 4.54577 


F 


0100100 


Variance 


(V) = 0.47200 





0111010 


Code No = 


27 



46 







Table 4.28 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


0101 


T 


1011011 


I 


0111 


1 


1110100 


A 


1000 


tf 


1110101 


E 


1010 


2 


1011000 


N 


1111 


) 


1011110 


R 


1100 


5 


1011001 


U 


00001 


3 


1011111 


L 


00010 


8 


1011100 


S 


00011 


( 


1011101 


K 


10010 


4 


1001110 


D 


00100 


• 
J 


1001111 


T 


00101 


9 


1110010 


M 


01000 


J 


mono 


Y 


01001 


6 


1110011 





01100 


W 


1110111 


G 


01101 


• 
• 


1110000 


B 


11010 


7 


1110001 


C 


11011 


- 


0000010 


) 


001110 


? 


0000011 


■ 


000000 


X 


00111100 


Z 


001100 


Q 


00111101 


V 


001101 






p 


0011111 


N = 11 , 


E = 0.00100 ; 


H 


1001100 


Mean Time 


I (L) = 4.56374 


F 


1001101 


Variance 


(V) = 0.51457 





1011010 


Code No = 


28 



47 







Table 4.29 






Various 


Codes for the Particular 


Alphabet (cont 'd. ) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1010 


» 




1001011 


I 


1011 


1 




1000000 


A 


1100 


If 




1000001 


E 


1101 


2 




1001000 


N 


1110 


) 




1001110 


R 


1111 


5 




1001001 


U 


00000 


3 




1001111 


L 


00001 


8 




1001100 


S 


00100 


( 




1001101 


K 


00010 


4 




1000100 


D 


00011 


> 




1000101 


T 


01000 


9 




1000010 


M 


01001 


J 




1000011 


Y 


01010 


6 




0010100 





01011 


W 




0010101 


G 


01100 


• 
• 




0011000 


B 


01101 


7 




0011001 


C 


OHIO 


- 




0011110 


3 


01111 


■ 




0011111 


• 


0011010 


X 




0011100 


Z 


0011011 


Q 




0011101 


V 


0010110 








P 


0010111 


N = 12 , 


E = 0.00250 ; 


H 


1000110 


Mean 


Time 


(L) = 4.58022 


F 


1000111 


Variance 


(V) = 0.60248 





1001010 


Code 


No = 


29 



48 







Table 4.30 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1001 


? 




0001101 


I 


1010 


1 




0110100 


A 


1011 


IT 




0110101 


E 


1100 


2 




1000010 


N 


1110 


) 




1000011 


R 


00000 


5 




0110000 


U 


00001 


3 




0110001 


L 


00010 


8 




1000000 


S 


00100 


( 




1000110 


K 


00101 


4 




1000001 


D 


00110 


• 
5 




1000111 


T 


00111 


9 




1000100 


M 


01000 


J 




1000101 


Y 


01001 


6 




0110110 





11110 


W 




0110111 


G 


11010 


• 
• 




0001110 


B 


OHIO 


7 




0110010 


C 


01111 


- 




0001111 


J 


010111 


• 




0110011 


• 


010100 


X 




0101100 


Z 


010101 


Q 




0101101 


V 


111110 








p 


mill 


N = 13 , 


E = 0.00100 ; 


H 


110110 


Mean 


Time 


i (L) = 4.60287 


F 


110111 


Variance 


(V) = 0.44151 





0001100 


Code 


NO = 


30 



49 







Table 4 


.31 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 




5YMB0L 


CODE WORDS 


space 


1001 




f 


011001 


I 


1010 




1 


111000 


A 


1100 




tt 


111001 


E 


1111 




2 


0000110 


N 


00010 




) 


0000111 


R 


00011 




5 


0111100 


U 


00100 




3 


0111101 


L 


00101 




8 


0111000 


S 


10111 




( 


0111001 


K 


00110 




4 


1011010 


D 


00111 




* 
9 


1011011 


T 


01101 




9 


0111010 


M 


01000 




J 


1011000 


Y 


01001 




6 


0111011 





01010 




W 


1011001 


G 


01011 




• 
• 


0111110 


B 


10000 




7 


0111111 


C 


10001 




- 


0000100 


) 


000000 




? 

■ 


0000101 


• 


110100 




X 


0000010 


Z 


110101 




Q 


0000011 


V 


110110 








p 


110111 


N 


= 12 , 


E = 0.00500 ; 


H 


111010 


M 


Ban Time 


i (L) = 4.66384 


F 


111011 


V 


ariance 


(V) = 0.40074 





011000 


C 


Dde No = 


31 



50 



Table 4.32 
Various Codes for the Particular Alphabet (cont'd.) 

SYMBOL CODE WORDS 
100111 

1 101100 
" 101101 

2 100010 
) 100011 

5 0111100 

3 0111101 

8 0111110 
( 0111111 

4 0110010 
0110011 

9 0110000 
J 0110001 

6 0001010 
W 0001011 
: 0001000 

7 0001001 
0001110 

? 0001111 
X 0001100 
Q 0001101 

N = 9 , E = 0.02000 ; 
Mean Time (L) = 4.68298 
Variance (V) = 0.42141 
Code No = 32 



SYMBOL 


CODE WORDS 


space 


1100 


I 


1101 


A 


1110 


E 


1111 


N 


OHIO 


R 


01101 


U 


10000 


L 


00000 


S 


00001 


K 


00100 


D 


00101 


T 


01000 


M 


01001 


Y 


01010 





01011 


G 


10100 


B 


10101 


C 


001110 


5 


001111 


• 


001100 


Z 


001101 


V 


101110 


P 


101111 


H 


100100 


F 


100101 





100110 



51 







Table 4.33 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1001 


» 


101110 


I 


1101 


1 


010101 


A 


1110 


tt 


101111 


E 


00000 


2 


110010 


N 


00100 


) 


110011 


R 


00101 


5 


110000 


U 


00110 


3 


110001 


L 


00111 


8 


101000 


S 


01000 


( 


101001 


K 


01001 


4 


0000100 


D 


01011 


• 
> 


0000101 


T 


01100 


9 


0001000 


M 


01101 


J 


0001001 


Y 


OHIO 


6 


0001010 





01111 


W 


0001011 


G 


10000 


• 
• 


0001110 


B 


10001 


7 


0001111 


C 


101010 


- 


0001100 


> 


101011 


? 

• 


0001101 


• 


101100 


X 


0000110 


Z 


101101 


Q 


0000111 


V 


111100 






p 


111101 


N = 15 , 


E - 0.00250 ; 


H 


111110 


Mean Time 


i (L) = 4.75953 


F 


111111 


Variance 


(V) = 0.37566 





010100 


Code No = 


33 



52 







Table 4 


.34 




Various 


Codes for the 


i Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 




SYMBOL 


CODE WORDS 


space 


1010 




f 


mill 


I 


1101 




1 


111100 


A 


1110 




It 


111101 


E 


00011 




2 


101100 


N 


01000 




) 


101101 


R 


00000 




5 


110010 


U 


00001 




3 


110011 


L 


00100 




8 


011100 


S 


00101 




( 


011101 


K 


00110 




4 


100010 


D 


00111 






100011 


T 


01010 




9 


100000 


M 


01011 




J 


100001 


Y 


01100 




6 


0100100 





01101 




W 


0100101 


G 


011110 




■ 
■ 


0001010 


B 


011111 




7 


0001011 


C 


110000 




- 


0001000 


J 


110001 




? 


0001001 


• 


101110 




X 


0100110 


Z 


101111 




Q 


0100111 


V 


100100 








p 


100101 


N 


= 13 , 


E = 0.01000 ; 


H 


100110 


M 


san Time 


i (L) = 4.79792 


F 


100111 


V 


ariance 


(V) = 0.42646 





111110 


C 


ode No = 


34 



53 







Table 4.35 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1011 


» 


111001 


I 


1100 


1 


111100 


A 


00010 


»f 


111101 


E 


00011 


2 


111010 


N 


00100 


) 


111011 


R 


00101 


5 


110100 


U 


00110 


3 


110101 


L 


00111 


8 


101000 


S 


OHIO 


( 


101001 


K 


01000 


4 


100010 


D 


01001 


> 


100011 


T 


01010 


9 


011110 


M 


01011 


J 


011111 


Y 


01100 


6 


0000010 





01101 


W 


0000011 


G 


10010 


• 
• 


0000000 


B 


10011 


7 


0000110 


C 


100000 


- 


0000001 


5 


100001 


9 

• 


0000111 


• 


101010 


X 


0000100 


Z 


101011 


Q 


0000101 


V 


110110 






P 


110111 


N = 16 , 


E = 0.00250 ; 


H 


111110 


Mean Time 


t (L) = 4.85151 


F 


111111 


Variance 


(V) = 0.31030 





111000 


Code No - 


35 



54 







Table 4.36 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1110 


f 




101011 


I 


1111 


1 




100100 


A 


00000 


?f 




100101 


E 


00001 


2 




100110 


N 


00011 


) 




110000 


R 


00100 


5 




100111 


U 


00111 


3 




110001 


L 


01000 


8 




101000 


S 


01010 


( 




110010 


K 


01100 


4 




101001 


D 


01101 


• 




110011 


T 


10001 


9 




110100 


M 


OHIO 


J 




110110 


Y 


01111 


6 




110101 





10110 


W 




110111 


G 


10111 


• 
• 




0011010 


B 


001100 


7 




0011011 


C 


000100 


- 




1000000 


i 


000101 


7 

m 




1000010 


m 


001010 


X 




1000001 


z 


001011 


Q 




1000011 


V 


010010 








p 


010011 


N = 21 , 


E = 0.0 ; 


H 


010110 


Mean 


Time 


i (L) = 4.8695 


F 


010111 


Variance 


(V) - 0.33162 





101010 


Code 


No = 


36 



55 







Table 4 


.37 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


< 


SYMBOL 


CODE WORDS 


space 


1110 




f 




100101 


I 


00000 




1 




110110 


A 


00001 




»f 




110111 


E 


00010 




2 




110000 


N 


00011 




) 




110010 


R 


00100 




5 




110001 


U 


00101 




3 




110100 


L 


00111 




8 




110011 


S 


01010 




( 




111100 


K 


01011 




4 




110101 


D 


01100 




• 
5 




111101 


T 


01101 




9 




111110 


M 


01111 




J 




mill 


Y 


10101 




6 




101000 





10000 




W 




101001 


G 


10001 




• 




0100100 


B 


10110 




7 




0100101 


C 


10111 




- 




1001110 


9 


010011 




? 




1001111 


• 


001100 




X 




0111000 


Z 


001101 




Q 




0111001 


V 


010000 










P 


010001 


N 


= 20 , 


E = 0.0 ; 


H 


100110 


M 


san 


Time 


i (L) = 4.93958 


F 


011101 


V 


ariance 


(V) = 0.20452 





100100 


C 


ode 


No = 


37 



56 







Table 4 


38 




Various 


Codes for the 


i Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


< 


SYMBOL 


CODE WORDS 


space 


1110 




f 


101101 


I 


1111 




1 


. 100010 


A 


00010 




It 


100011 


E 


01010 




2 


101110 


N 


01011 




) 


110010 


R 


01100 




5 


101111 


U 


01101 




3 


110011 


L 


OHIO 




8 


110000 


S 


01111 




( 


110001 


K 


10010 




4 


101000 


D 


10011 




■ 

> 


101001 


T 


11010 




9 


000000 


M 


11011 




J 


001000 


Y 


001010 




6 


000001 





001011 




W 


001001 


G 


000010 




• 
• 


001110 


B 


000011 




7 


001111 


C 


010010 




- 


001100 


J 


010011 




? 


001101 


• 


010000 




X 


000110 


Z 


010001 




Q 


000111 


V 


101010 








p 


101011 


N 


= 13 , 


E = 0.02000 ; 


H 


100000 


M( 


san Time 


> (L) = 4.94386 


F 


100001 


V 


ariance 


(V) = 0.41804 





101100 


C 


Dde No = 


38 



57 







Table 4.39 




Various 


Codes for the Particular Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1111 


1 


011000 


I 


00000 


1 


001001 


A 


00001 


If 


011110 


E 


01011 


2 


011001 


N 


00010 


) 


100010 


R 


00011 


5 


011111 


U 


00101 


3 


100011 


L 


00110 


8 


100100 


S 


00111 


( 


110010 


K 


01000 


4 


100101 


D 


01001 


• 


110011 


T 


10100 


9 


110000 


M 


10101 


J 


110001 


Y 


10110 


6 


110110 





10111 


W 


110111 


G 


11100 


; 


110100 


B 


11101 


7 


110101 


C 


100000 


- 


0101010 


) 


100001 


? 


0101011 


• 


100110 


X 


0101000 


z 


100111 


Q 


0101001 


V 


011100 






p 


011101 


N = 10 , 


E = 0.02000 ; 


H 


011010 


Mean Time 


t (L) = 4.95533 


F 


011011 


Variance 


(V) = 0.22069 





001000 


Code No = 


39 



58 







Table 4 


40 






Various 


Codes for the Particular 


Alphabet (cont'd.) 


SYMBOL 


CODE WORDS 


SYMBOL 


CODE WORDS 


space 


1111 




1 




101101 


I 


00000 




1 




110010 


A 


00001 




t» 




110011 


E 


01010 




2 




101110 


N 


00011 




) 




101111 


R 


00110 




5 




000100 


U 


00111 




3 




111010 


L 


10000 




8 




000101 


S 


10001 




( 




111011 


K 


10010 




4 




111000 


D 


10011 




• 
9 




111001 


T 


10100 




9 




011010 


M 


10101 




J 




011011 


Y 


11010 




6 




011000 





11011 




W 




011001 


G 


001000 




• 
• 




011110 


B 


001001 




7 




011111 


C 


001010 




- 




011100 


5 


001011 




•> 

• 




011101 


• 


010010 




X 




010110 


Z 


010011 




Q 




010111 


V 


010000 










p 


010001 


N 


= 11 , 


E = 0.02500 ; 


H 


110000 


M( 


san 


Time 


t (L) = 4.99572 


F 


110001 


V 


ariance 


(V) = 0.26248 





101100 


C 


Dde 


No = 


40 

. 



59 



III. THE EVALUATION OF RESULTS 

To gain a better understanding of the relative merits of 
the various experimental codes, a graph of their respective 
mean times and variances is given in Figure 3.1. The figure 
emphasizes that a small increase in mean time can result in 
a marked reduction in variance. The dotted line represents 
the minimum variance found for the corresponding mean time, 
and the boxes correspond to experimental codes which meet 
the minimum variance criteria. 

Figure 3.2 also displays the experimental codes which 
have minimum variance for a given mean time. The points 
numbered 1 through 12 correspond to the codes given in 
Tables 4.1 through 4.12. This figure includes the Huffman 
code and the block code as the extreme points. The Huffman 
code represents minimum mean time and maximum variance while 
the block code has zero variance but greatly increased mean 
time. (For an alphabet of 47 letters Block Coding Gives an 
average length of 6 with zero variance). 

The data for the figures appears in Table 5. This table 
also gives a summary of the reductions in variance achiev- 
able, with the differing amounts of mean time for the 
particular alphabet. The Huffman code is used as the base 
for computing the increments in mean times and the decre- 
ments in variances of these codes . 



60 






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63 



Using the same table, a graph of the sacrifice in mean 
time versus the decrease in variance is given in Figure 3.3. 
Note that the graph includes segments almost parallel to the 
axis. These parallel segments simply show that further 
attempts at optimization are redundant for little gain in 
one variable causes significant loss in the other (Note that 
the segment between the Huffman code and code 2 is almost 
parallel to the vertical axis and the segment between code 
12 and the block code is almost parallel to the horizontal 
axis). Consequently, better mixes of mean time and vari- 
ance can be obtained using the segment between code 2 and 
code 12. 

The selection of the codes depends on the output rate 
required. The term output rate is defined as the capacity 
of a processor for handling the traffic. The output rate of 
an On-Line communications device should be chosen so that on 
the average it can handle the input rate. When variations 
occur communications processors put the excess digits (0 and 
1) in a buffer. These excess digits are later transmitted 
on the first in first out (FIFO) basis. The size of the 
FIFO buffer should be chosen to accomodate the maximum queue 
length. If, under extreme conditions, this is exceeded 
overflow is said to have occured, and some digits may be 
lost. The buffer size gives a further way of selecting 
among the various codes . 

An example is included to find the maximum number of 
digits in the buffer during the transmission of two articles 
given in Appendix A. There are only two absolute rates 
available to be chosen as output rate, Huffman and Block 
code, and the latter would give little insight into the 
problem. For this example, the output rate chosen is 
4.30771 bits per unit time representing the minimum mean 
time for the particular alphabet, obtained by Huffman 
Coding. Each code in Table 5 is then used to transmit the 



64 




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65 



magazine articles so that their respective buffer require- 
ments could be. determined. The Statistical Analysis System 
(SAS) program used by the author for this purpose is given 
in Appendix C. The result of the experiment is summarized in 
Table 6 and a graph of the maximum buffer length versus the 
mean time is given in Figure 3.4. 









TABLE 


6 






Maximum Buffer 


Length for 


Minimum Out] 


put Rate 






Output Rate = 4.30771 bits/unit 


time 












Maximum 


Code No 
Huffman 


Table No 
3 


Mean time 
4.30771 


Variance 
1.91828 


Buffer Length 


66 


1 




4 


4.31277 


1.41646 


52 


2 




4.1 


4.3194 


1.3444 


47 


3 




4.2 


4.36186 


0.93749 


42 


4 




4.3 


4.4168 


0.68287 


62 


5 




4.4 


4.45705 


0.52959 


68 


6 




4.5 


4.53922 


0.45146 


97 


7 




4.6 


4.58711 


0.42911 


176 


8 




4.7 


4.65856 


0.38929 


261 


9 




4.8 


4.73389 


0.34297 


1468 


10 




4.9 


4.82519 


0.28005 


3102 


11 




4.10 


4.92818 


0.1933 


4945 


12 




4.11 


5.06011 


0.05707 


7305 


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67 



The results show that using code 3 (which is given in 
Table 4.3) gives the best result in terms of minimum delay 
incurred during the transmission of the articles. Although 
Huffman Coding produces the minimum average length code, 
because of its large variation, it causes more delay at some 
part of the transmission than code 3. This shows that an 
urgent short message may take much longer than expected as a 
result of the large variance. 

Bear in mind that the maximum buffer size depends on two 
effects. First, except for the Huffman code, we are trying 
to send more than the rate can handle, and hence there is a 
linear growth of the buffer size with the length of the 
message. Second, the buffer size depends on the variance, 
and with longer messages we expect that the maximum fluctua- 
tion will grow like the square root of the message length. 
Table 6 clearly demonstrates that near Huffman Code the gain 
due to the drop in variance is greater (for this length 
message used) than the loss due to the increase in the mean 
time . 

Any other output rate can be chosen between the mean 
times of Huffman and Block codes and the same experiment can 
be conducted. Five output rates were arbitrarily chosen by 
the author and the obtained results are summarized in Table 
7. Note that as the desired output level is increased the 
codes which give the best results shift from code 3 towards 
code 12, getting further apart from the Huffman code. 

Once again, remember that optimum point of a subsystem 
may be less significant than the optimum of the system as a 
whole. Often system performance is spoiled when a partic- 
ular aspect is optimized. For Huffman coding the optimiza- 
tion for minimum average length causes a large variance. 
The thesis is an example of the general rule that when one 
aspect has been optimized it is to the detriment of most 
other aspects of the system, and optimizing for minimum 



68 







TABLE 


7 










Maximum Buffer 


Length for 


Different 


Output 


Rat 


es 




Output rates are given in 


bits/unit 


time 


below. 


Code No 


4.4 


4.5 


4.6 




4.7 




4.8 


Huffman 


58 


54 


51 




48 




45 


1 


48 


44 


41 




38 




35 


2 


44 


40 


37 




34 




31 


3 


38 


34 


31 




28 




25 


4 


42 


38 


35 




32 




29 


5 


36 


30 


26 




23 




20 


6 


42 


26 


22 




19 




15 


7 


63 


28 


23 




20 




16 


8 


115 


36 


19 




15 




12 


9 


211 


77 


25 




18 




12 


10 


1343 


187 


57 




22 




15 


11 


3185 


1278 


177 




59 




18 


12 


5545 


3638 


1731 




226 




81 


Block CO 


de 22365 


20457 


18550 




16643 




14736 



length produced a large variance. It was natural to suspect 
that by giving up a little in the mean time could result, if 
done properly, in a great gain (near the optimum) in the 
reduction of variance. 



69 



APPENDIX A 
THE MAGAZINE ARTICLES AND PROGRAMS 

A. THE MAGAZINE ARTICLES 

Because this research is for an On-Line system, it is 
important to include the frequency of spaces in the text. 
To allow for this in the program, slashes were used instead 
of spaces . 

The first article titled "Strange Shapes of Modern 
Ships" is given below (the slashes between the words are not 
shown) . 

BIR DERGININ RESSAMI, EN GUCLU VINCLERIN YAPAMADIGI ISI 
BASARARAK, 50.000 TONLUK BIR "OKYANUS DEVI"NI SUDAN CIKARDI 
VE BOYLECE, GEMININ BURNUNDAKI YUMRUBAS "BALB" ORTAYA CIKMIS 
OLDU. GEMININ KIC TARAFINDA DA BAZI YENILIKLER GOZE 
CARPIYORDU. BUNLARIN SIRRI ACABA NE OLABILIRDI? OTOMOBIL 
YAPIMCILARININ YENI GELISTIRDIKLERI MODELLERI DENEDIKLERI 
"RUZGAR TUNELLERI"NIN BIR BENZERI DENIZ TEKNELERI UZERINDE 
CALISAN MESLEKDASLARI ICIN DE GECERLI OLUYOR. ONLARIN DA 
YENI TEKNE MODELLERINI DENEDIKLERI "TEST HAVUZLARI" VAR. 
YENI GEMILER, ANCAK, BU HAVUZLARDA YAPILAN DENEYLERIN OLUMLU 
SONUCLAR VERMESINDEN SONRA, INSA EDILMEK UZERE KIZAGA 
KONUYOR. BU ARADA, GEMI MUHENDISLERININ ISLERI, KARA 
ARACLARI UZERINDE UGRAS VEREN MESLEKDASLARININ ISLERINDEN 
BIRAZ DAHA GUC . BU GUCLUK , DAHA MODEL ASAMASINDA BASLAR. 
DENEYLERI YAPILAN GEMI MODELLERI, YETERINCE BUYUK OLDUGU 
ZAMAN, DENEYLERDEN ALINAN OLCUM SONUCLARI , ISTENILENI 
VEREBILMEKTEDIR. GUCLUGU YARATAN IKINCI ETKEN DE , DUNYAMIZIN 
"SU" VE 'HAVA' OLARAK BILINEN IKI ELEMANINDAN 
KAYNAKLANMAKTADIR. BIR KARA TASITINDA, KAROSERI SADECE 
RUZGARA KARSI KOYMAK ZORUNDA OLMASINA KARSIN, BIR TEKNENIN 



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HEM DALGAYA VE HEM DE , RUZGARA KARSI KOYMASI GEREKIR. ESKI 
TARIHLERDE INSA EDILMIS GEMILERDE, BURUNLAR KESKINLESTIRILIR 
VE BOYLECE SUYUN DAHA AZ BIR DIRENIMLE YARILMASI SAGLANIRDI . 
ANCAK, BU IS, ASLINDA HIC DE GORUNDUGU KADAR BASIT DEGILDIR. 
GEMI HESAPLARI, SUALTINDAN ATESLENEN BIR ROKETIN 
HESAPLARINDAN DAHA KARMASIK VE GUCTUR. BIRAZ ONCE 
BELIRTTIGIMIZ GIBI BIR GEMI, SU VE HAVA ORTAMINDA SEYREDER. 
BU NEDENLE DE , OZELLIKLE HAVANIN VE SUYUN BIRLESTIGI NOKTA, 
MUHENDISLER ICIN BIR "BILMECE"DIR. DENEY HAVUZLARINDAN 
ALINAN SONUCLAR OKYANUSLAR ICIN DE GECERLI OLDUGUNDAN ; BU 
BENZER ILISKILERDEN YARARLANAN GEMI MUHENDISLERI , 
DENEYLERINI DENEY HAVUZLARINDA YAPMAKTADIRLAR . GEMIYE 
HAREKET VEREN PERVANE , TEKNEYI ILERIYE ITERKEN, GEMININ 
BURNUNDA BIR DALGA OLUSUR. BU DALGA, BURUNDA, YANLARDA , 
DIPTE VE KICTA GEMIYI YALAYARAK GECER. ANCAK, ANILAN DALGA 
ALISILAGELEN TIPTE BIR DALGA OLMAYIP , SAGA- SOLA KARISIK 
HAREKETLER YAPAN SULAR HALINDEDIR. GEMI BURNUNDA OLUSAN VE 
TEKNE TARAFINDAN ILETILEN BU SU KITLELERI , GEMI BURNUNUN 
GENISLIGI ORANINDA ARTAN BIR YIGILMA YAPARAK , ISTENILMEYEN 
BIR DIRENC OLUSTURUR (SEKIL 1). ISTENILMEYEN BU DIRENCIN 
ETKISINI AZALTABILMEK ICIN, GEMININ BURNUNDA YUMRUBAS 
DENILEN VE MAHMUZU ANDIRAN BIR CIKINTI YAPILIR. YUMRUBASIN 
ETKISI SOYLE ACIKLANABILIR: YUMRUBASLI BIR TEKNE, ONUNDE 
IKI DALGA TEPESI OLUSTURUR. BUNLARDAN , TEKNENIN OLUSTURDUGU 
DALGA TEPESI, YUMRUBASIN OLUSTURDUGU DALGANIN CUKURUNU 
DOLDURARAK, GEMI BURNUNDAKI YIGILMAYI ONLER. (SEKIL 2) SONUC 
OLARAK DA, ISTENILMEYEN DALGA YOK EDILIR. YUMRUBAS ADI 
VERILEN BU YENI BURUN TIPI , AMERIKALI GEMI DAVID TAYLOR"UN 
BULUSUDUR. YUZYILIMIZIN BASLARINDA TAYLOR, YUMRUBASLI 
GEMILERIN, DIGERLERINE KIYASLA DAHA KUCUK DALGALAR 
OLUSTURDUGUNU TESPIT ETMIS VE BUNUN TEORISI DAHA SONRA 
GELISTIRILMISTIR. ANCAK, TUM OLASILIKLARI AYDINLIGA 
KAVUSTURACAK KESIN FORMULLER GUNUMUZDE DAHI TAM OLARAK 
SAPTANMIS DEGILDIR. YUMRUBAS TEORISININ GELISMESINI 



71 



ASAGIDAKI MADDELERLE ACIKLAYABILIRIZ : 1. SEYIR HALINDEKI BIR 
GEMI, ONUNDE BUYUK BIR DALGA TEPESI OLUSTURARAK ILERLER. 2. 
SU YUZEYININ HEMEN ALTINDA HAREKET ETTIRILEN BIR KURE , 
ARKASINDA BIR DALGA CUKURU OLUSTURUR. 3. GEMI MODELININ 
BURNUNA BIR KURE YERLESTIRILEREK , KURENIN OLUSTURDUGU DALGA 
CUKURU ILE GEMI MODELININ OLUSTURDUGU DALGAYI CAKISTIRACAK 
BIR DENEY UYGULAMASI GERCEKLESTIRILIR. 4. DENEYDE , DALGA 
CUKURUNUN DALGA TEPESINI YUTTUGU GORULUR. 5. DALGA TEPESI 
YUTULDUGUNDAN ; ISTENILMEYEN DIRENC ETKISINI KAYBEDER. SONUC 
OLARAK, GEMI MODELI DAHA BUYUK BIR HIZ KAZANIR VEYA HAREKETI 
ICIN GEREKLI OLAN GUC AZALIR. ALINAN BU SONUC, GEMININ 
TUKETTIGI YAKITTA HIC DE AZIMSANAMAYACAK BIR TASARRUF 
SAGLANDIGINI ORTAYA KOYAR. ARMATORLERIN YUMRUBASLI GEMI 
SIPARISLERINE AGIRLIK VERMELERINDEN SONRA, MUHENDISLERIN 
ISLERI DAHA DA GUCLESMISTIR. ILK ZAMANLARDA YUMRUBASLAR, 
YOLCU VE SAVAS GEMILERINDE UYGULANIYORDU . BUNUN DA NEDENI , 
ANILAN GEMILERIN SEFERLERINI GENELLIKLE SABIT BIR SU 
KESIMINDE YAPMALARI IDI . OYSA, ARMATORUN SIPARISE BAGLADIGI 
YUK GEMILERINDE SU KESIMI (DRAFT), GEMILERIN YUKLU VEYA BOS 
OLMALARINA GORE, DEGISEBILDIGI ICIN, GEMI BURNUNDA YER ALAN 
YUMRUBAS, ETKINLIK POZISYONUNU KORUYAMAMAKTADIR. GEMI, 
YUKUNU ALARAK SEFERE CIKTIGINDA; YUMRUBAS, SUALTINDA, 
KALARAK, ETKINLIGINI SURDURMEKTE ISE DE , YUKUN 
BOSALTILMASINDAN SONRA, SU YUZEYINE CIKMAKTA VE SONUC 
OLARAK, ETKINLIGINI KAYBETMEKTEDIR. BU DURUM, YUMRUBASIN 
GEMI BURNUNDA NEREDE YER ALMAS I GEREKTIGI SORUNUNU ORTAYA 
CIKARMISTIR. DAHA SONRA, YUMRUBAS, GEMI BURNUNUN BIRAZ DAHA 
ASAGISINA ALINARAK, SUYUN ALTINDA BIRAKILMIS VE ISTENILEN 
SONUCA KISMEN DE OLSA ULASILMISTIR. YUMRUBASI SADECE 
SUALTINDA BIRAKMAKLA SORUNLARA COZUM GETIRILEMEMEKTEDIR. 
CUNKU, HER TEKNE KENDINE OZGU BIR DALGA SEKLI OLUSTURMAKTA 
VE BU NEDENLE DE , YUMRUBASIN, KULLANILACAGI TEKNE ILE UYUM 
SAGLAYACAK OZELLIKLERE SAHIP OLMASI GEREKMEKTEDIR . GEMI 
MUHENDISLERININ GOGUSLEMEK ZORUNDA OLDUKLARI BU GUCLUKLER, 



72 



YENI ARASTIRMA ALANLARININ DOGMASINA YOL ACMIS VE BU KEZ DE , 
ARASTIRMALAR GEMININ KIC TARAFINDA YOGUNLASMISTIR. YAKLASIK 
20 YIL KADAR ONCE, HAMBURGLU GEMI MUHENDISI ERNST NONNECKE , 
YENI BIR KIC FORMU GELISTIRMIS ISE DE , ONUN BU BULUSU ANCAK 
SON YILLARDA DEGER KAZANMAGA VE DIKKAT CEKMEGE BASLAMISTIR. 
NITEKIM, NONNECKE 'NIN BULUSU, BIR KORE TERSANESINDE 2 
KONTEYNER GEMISINDE UYGULAMAYA KONULMUSTUR. TEORIK 
CALISMALAR HAMBURG"DA BASLAMIS VE BUNU IZLEYEN DENEYLERDE , 
INSA EDILECEK GEMININ BIR MODELI , BOYU 300 M. VE DERINLIGI 
18 M. OLAN BIR DENEY HAVUZUNA CEKILEREK , NONNECKE 'NIN 
GELISTIRDIGI KIC FORMUNUN USTUNLUGU KABUL EDILMISTIR. BU TIP 
ASIMETRIK KIC FORMU: SANCAK TARAFI CUKUR VE ISKELE TARAFI 
DISA DOGRU BOMBELIDIR. BU FORMUN OZELLIGI , SUYUN AKISINI 
DUZELTEREK, DOGRUDAN PERVANEYE VERMESIDIR. NONNECKE TIPI 
KIC FORMU TEORISI SU SEKILDE ACIKLANABILIR: SIVI ICINDE 
HAREKET EDEN BIR GOVDE , SUYU BAS TARAFINDAN YARAR . YARILAN 
SU, GOVDENIN KIC TARAFINDA YINE BIRLESMEK EGILIMI 
GOSTERIRKEN, BU KEZ DE GEMININ PERVANESI ILE KARSILASIR. 
GEMININ HAREKET YONUNE GORE, SAGA DOGRU DONEN PERVANE , SUYU 
TEKNENIN SANCAK (SAG) TARAFINDAN ASAGIYA ITER, BUNA KARSIN, 
ISKELE TARAFINDAN (SOL), YUKARIYA DOGRU ITILEREK, TEKNENIN 
KIC TARAFINDA BIRLESME EGILIMI GOSTEREN SU, BIRLESEMEDEN 
PERVANENIN AKIMINA KAPILIR. CEKILEN SUALTI FOTOGRAFLARI ILE 
TESPIT EDILEN BU OLAY , SUYUN GEMIDE ISKELE TARAFININ 
GEREKTIRDIGI ITICI GUCU OLUSTURAMADAN , YUKARIYA DOGRU 
ITILDIGI GERCEGINI ORTAYA KOYMUSTUR. BU OLAY UZERINDE DURAN 
NONNECKE, ISKELE TARAFINDAN PERVANEYE YONELEN SU AKISINI 
DUZENLEYEBILMEK ICIN GEMIDE SANCAK VE ISKELE TARAFLARININ 
PERVANEYE YAKIN OLAN KISIMLARINDA, TASARLADIGI FORM 
DEGISIKLIKLERINI GERCEKLESTIRMISTIR. BUNA GORE, GEMININ 
SANCAK TARAFI CUKURLASTIRILMIS ; ISKELE TARAFINDA ISE, 
CUKURLUGUN YERINI YUMUSAK BIR BOMBE ALMISTIR (SEKIL 5). 
SONUC OLARAK, SUYUN DAGILMAKSIZIN VE TURBULANSA 
UGRAMAKSIZIN, PERVANEYE AKABILMESI SAGLANMISTIR. SEKIL 3 VE 



73 



5 ESKI VE YENI TIP IKI GEMININ EN KESIT EGRILERINI 
VERMEKTEDIR. ESKI TIP BIR GEMIDE EN KESIT EGRILERI SIMETRIK 
BIR BICIM GOSTERMEKTE VE GEMININ ORTASINDA DUZ BIR CIZGI 
BOYUNCA BIRLESMEKTEDIR (SEKIL 3). DIGER TIP KIC FORMUNDA 
ISE, ANILAN EGRILER ASIMETRIK OLARAK GELMEKTE VE GEMININ 
ORTASINDA "S" SEKLINDEKI BIR CIZGI UZERINDE TOPLANMAKTADIR 
(SEKIL 5). SEKIL 4 VE 6 ' DA , ESKI VE YENI TIP KIC 
FORMLARININ BIRER PROFILI ILE PERVANEYE DOGRU YONELEN SUYUN 
AKISI GORULMEKTEDIR. ESKI TIP KIC FORMUNDA (SEKIL 4); 
PERVANEYE DOGRU AKIS YAP AN SU , PERVANE ILE KARSILASTIGINDA 
TURBULANSA UGRAMAKTA VE DOLAYLI OLARAK DA, GEMI DIESELININ 
PERVANEYE AKTARDIGI GUCTE KAYIBA YOL ACMAKTADIR. NONNECKE 
TIPI KIC FORMUNDA ISE, PERVANEYE YONELEN SUYUN AKISI 
DUZENLENMIS (SEKIL 6) VE DUZENLENEN SU, TURBULANSA 
UGRAMADAN, PERVANE TARAFINDAN ITILEREK, PERVANENIN VERIMI 
ARTIRILMIS VE GEMININ DAHA AZ BIR GUCLE DAHA BUYUK BIR HIZ 
KAZANMASI SAGLANMISTIR. "THEA S" ADLI 124 METRELIK GEMIDE 
YAPILAN DENEYLER, BU YENI KIC FORMUNUN GUNDE 2.000 LITRELIK 
BIR YAKIT TASARRUFU SAGLADIGINI ORTAYA KOYMUSTUR. ESKI TIP 
GEMI FORMLARININ GECERLI OLDUGU GUNLERE KIYASLA, YAKIT 
FIATLARININ BUGUN 10 KAT ARTTIGI GOZ ONUNDE TUTULURSA, 
GEMILERE SAGLANAN YAKIT TASARRUFUNUN NE KADAR ONEMLI OLDUGU 
VE MODERN GEMILERIN NICIN BOYLE GARIP BICIMLERDE INSA 
EDILDIGI SORUSU KENDILIGINDEN AYDINLIGA KAVUSABILIR. 

The second article titled "Story of the Space Shuttle" 
is given below (the slashes between the words are not 
shown) . 

19 70 'LERE DEK DAYANAN UZAY MEKIGI PROJESININ TEMEL AMACI , 
UZAYA DAHA UCUZ VE DOLAYISIYLA DAHA SIK GITMEKTIR. MEKIKTEN 
ONCE UZAYA ATILAN INSANLI VE INSANSIZ UYDULAR, SONDA VE 
ROKETLER SADECE BIR KEZ KULLANILABILIYORDU VE BU NEDENLE 
MALIYETLERI YUKSEK OLUYORDU . UZAY MEKIGI PROJESI ILE 
INSANOGLU, AYNI UZAY ARACINI SUREKLI KULLANMA OLANAGINA 



74 



KAVUSTU. BU PROJENIN EN BELIRGIN OZELLIGI UCAK TEKNOLOJISI 
ILE UZAY TEKNOLOJISINI BIR ARAYA , GETIRMESIDIR. SISTEM 
GENELDE UC ANA BOLUMDEN OLUSMAKTADIR: 1) YORUNGE ARACI DA 
DENEN UZAY GEMISININ KENDISI; 2) BUYUK DIS YAKIT TANK I ; 3) 
DIS YAKIT TANKININ HER IKI YANINDA BULUNAN KATI YAKITLI 
ROKETLER. SISTEMI FIRLATMA ANINDA, GEMININ ARKASINDA BULUNAN 
ANA MOTORLAR VE IKI FIRLATICI ROKET ATESLENIR. BU ISLEMIN 
SONUNDA, OTUZ MILYON NEWTON ' LUK COK BUYUK BIR FIRLATMA 
KUVVETI, SISTEMI HAVALANDIRIR. HAVALANDIKTAN BIR DAKIKA 
SONRA SISTEMIN SURATI , SES SURATINI ASAR. BU SIRADA GEMININ 
ICINDE OLSANIZ VE KENDINIZI TARTSANIZ, YERYUZUNDE 60 KILO 
GELEN VUCUDUNUZUN, IKI DAKIKA ICINDE SISMANLAMIS OLMAMASINA 
KARSIN, 180 KILO GELDIGINI GORURSUNUZ . BU ILGINC DURUM, 
ARACIN IVMESININ, CEKIM IVMESINDEN UC KAT FAZLA OLMASINDAN 
KAYNAKLANMAKTADIR. HAVALANDIKTAN SONRA KATI YAKITLI 
ROKETLERIN YAKITLARI BITER VE DIS YAKIT TANKINDAN 
AYRILIRLAR. BU ANDA GEMI , 50 KM. YUKSEKLIKTE VE HIZI SAATTE 
5.000 KM 'YE ULASMISTIR. AYRILAN ROKETLER, ILK HIZLARINDAN 
DOLAYI DERHAL ASAGIYA DUSMEZLER. 50 KM'DE AYRILAN BU 
ROKETLER, 6 7 KM ' YE DEK CIKAR VE SONRA DUSMEYE BASLAR. 
DUSERKEN, YUZEYDEN YAKLASIK 3 KM. YUKSEKLIKTEN , UC EVRELI 
PARASUT SISTEMI CALISIR VE DUSUSUN HIZINI AZALTIR. DENIZE 
DUSEN ROKETLER, SU YUZEYINE DEGDIKLERI ANDA PARASUTLERDEN 
AYRILIR VE ALT TARAFTA BULUNAN OZEL BOLMELER SISEREK, 
ROKETLERIN BATMAMALARI SAGLANIR. DAHA SONRA BUNLAR DENIZDEN 
TOPLANIR, GEREKLI ONARIM VE BAKIM YAPILARAK, BIR SONRAKI 
UCUS ICIN HAZIRLANIRLAR. BU KATI YAKITLI ROKETLERIN 
KALKISTAKI AGIRLIGI , YAKLASIK 580 TONDUR VE 11.800.000 
NEWTON 'LUK BIR ITME MEYDANA GETIRMEKTEDIR. UZUNLUGU 45.5 
METRE, SILINDIRIK GOVDENIN CAPI ISE 3.7 METREDIR. UZAY 
GEMISININ ANA MOTORLARINA YAKIT VEREN BUYUK DIS TANK ISE 
YERDEN 200 KM. YUKSEKLIKTE IKEN YAKITI BITTIGINDE ARACTAN 
AYRILIR. 20 KATLI BIR APARTMAN YUKSEKLIGINDE (50. M) OLAN BU 
BUYUK SILINDIRIK TANKIN CAPI 30 METREDIR. YAPIMI ICIN 30 TON 



75 



ALUMINYUM KULLANILAN BU TANKIN BIR KEZ KULLANILMASI , BIRCOK 
KISININ NASA'YI ELESTIRMES JNE NEDEN OLMAKTADIR. CUNKU 
MEKIKTEN AYRILAN TANK, DAHA SONRA DUNYA ATMOSFERINE GIREREK 
YANMAKTADIR. NASA MUHENDISLERI BU TANKLARDAN NASIL 
YARARLANACAKLARINI DUSUNMEKTEDIRLER. HAZIRLANAN BIR PROJEYE 
GORE, 1990 'DAN SONRA KURULMASI BEKLENEN UZAY ISTASYONUNUN , 
BU TANKLARDAN YIRMISININ BIR ARAYA GETIRILEREK YAPILMASI 
ONERILMEKTEDIR. MARTIN MARIETTA AEOROSPACE SIRKETI'NIN 
GELISTIRILMIS PROGRAMLAR BASKANI OLAN FRANK WILLIAMS 'A GORE 
GEMI, TANKINI UZAYDA BIRAZ DAHA SONRA BIRAKACAK. ZAMAN 
TANK, YER ATMOSFERINE DUSMEYECEK, GEMIYI IZLEYEREK ISTENEN 
YORUNGEYE OTURTULMASI SAGLANACAK . DENEYLERIN YAPILACAGI VE 
ICINDE RAHATCA YASANABILECEK SAGLAMLIKTA OLAN BU SILINDIRLER 
UC UCA EKLENDIGINDE, ISTENEN UZAY ISTASYONUNUN HEM DAHA KISA 
ZAMANDA, HEM DE DAHA EKONOMIK BIR SEKILDE YAPILABILECEGI 
ILERI SURULUYOR. UZAY GEMISININ ON GOVDESI VE MURETTEBAT 
BOLUMU, ALUMINYUMDAN YAPILMIS UC KATTAN OLUSMAKTADIR. EN UST 
KATTA, YORUNGE ARACININ KENDISINI , TUM UZAY GEMISI SISTEMINI 
VE TASINAN YUKU YONETEN , DENETLEYEN KUMANDA SISTEMI YER 
ALMAKTADIR. BU KATTA, UC ASTRONOT ISKEMLESI BULUNMAKTADIR. 
ORTA KAT, UCUS UZMANI TASIMA VE YASAM BOLUMU OLARAK 
AYRILMISTIR. AYRICA BU BOLUM, GEMININ YUK TASIYAN KARGO 
BOLUMU ILE BAGLANTILIDIR. ALT KATTA ISE CEVRE KONTROL 
GERECLERI YER ALMAKTADIR. GEMININ ORTA BOLUMU, YUK TASIYAN 
KARGO BOLUMUDUR VE UZAYA GIDERKEN USTTEN ACILAN IKI KAPAK 
ILE ORTULMEKTEDIR. UZAYDA BU KAPAKLAR ACILARAK, UYDULARI 
YORUNGEYE OTURTMAK , YURUYUS YAPMAK GIBI CESITLI GOREVLER 
YERINE GETIRILMEKTEDIR. ARKA GOVDE VE MOTOR YUVALARINI 
TASIYAN SON BOLUM, YORUNGE ARACININ EN KARMASIK PARCASIDIR. 
SADECE 8 DAKIKA SUREYLE ATESLENEN VE YORUNGEYE ERISMEZDEN 
ONCE 6 MILYON NEWTON ' LUK FIRLATMA KUVVETI YARATAN UC ANA 
MOTOR BU BOLUMDEDIR. ANA MOTORLAR SUSTUKTAN SONRA GEMIYI 
YORUNGESINE OTURTAN IKI ROKETTEN OLUSAN YORUNGE MANEVRA 
SISTEMI DE BU ARKA BOLUMDEDIR. SON OLARAK BU BOLUMDE 38 'I 



76 



ANA, 6 'SI DUYARLI OLMAK UZERE TOPLAM 44 KUCUK ROKETTEN 
OLUSMUS, TEPKI-DENETIM SISTEMI BULUNMAKTADIR. BU SISTEM, 
ARACIN (YORUNGE ICINDE KALMA KOSULU ILE) KONUMUNU VE UC 
EKSENI BOYUNCA DONME HAREKETLERINI SAGLAMAKTADIR. YUKARIDA 
KISACA OZELLIKLERINI TANITMAYA CALISTIGIMIZ UZAY GEMISI ILK 
UZAY UCUSUNU, 3 YILLIK BIR GECIKMEDEN SONRA, 1981 YILINDA 
YAPTI. UCUSA HAZIRLANAN 4 UZAY GEMISINDEN ILK YAP I LAN I , 
COLOMBIA ADINI TASIYORDU. UCUS KOMUTANI VE PILOT, ILK GEMI 
SEYRININ PERSONELIYDILER. 12 NISAN 1981 GUNU COLOMBIA 
FLORIDA' DAKI FIRLATMA USSUNDEN HAVALANDI . DUNYA CEVRESINDE 
36 TUR ATAN GEMI KALKISTAN 54.5 SAAT SONRA, 14 NISAN GUNU 
YERYUZUNE DONDU . UCUS BASARILI GECMISTI AMA; GEMIYI YUKSEK 
SICAKLIKTAN KORUYAN KORUMA FAYANSLARI ONEMLI DERECEDE HASARA 
UGRAMISTI. HASARA NEDEN OLAN SICAKLIK, OZELLIKLE ARAC 
DUNYA 'YA DONERKEN, ATMOSFERDEKI SURTUNMEDEN KAYNAKLANIYORDU . 
IKINCI UCUS, 14 KASIM 1981 GUNU GERCEKLESTIRILDI . BES GUN 
OLARAK DUSUNULEN UCUS PROGRAMI YARIDA KESILDI VE GEMI IKI 
GUN SONRA YERYUZU'NE DONDU. BU UCUSUNDA HAVA KIRLILIGI , 
DENIZ ARASTIRMALARI GIBI BIR TAKIM BILIMSEL ARASTIRMALAR 
YAPILDI. AYRICA, KANADALILARIN YAPTIGI HERHANGI BIR YONE 
DOGRU 15.6 METRE UZANABILEN, GEMI DISINDAKI BIR NESNEYI 
TUTMAK ICIN VEYA ICINDEKI BIR ALETI TUTUP UZAYA BIRAKABILMEK 
ICIN KULLANABILECEK, KIMININ VINC , KIMININ ROBOT, 
BAZILARININ DA MEKANIK KOL DEDIGI BIRIMI DENEDILER. BU 
UCUSTA GEMI, BIRINCIYE GORE DAHA AZ HASARA UGRAMISTI. UCUNCU 
UCUS, 22 MART 1982 GUNU BASLADI VE ILK KEZ SEKIZ GUN SURDU . 
GEMI, PLANLANAN SEYRINI BIR GUN GECIKMEYLE 30 MART ' TA 
TAMAMLADI. BU SEYIRDE , KOMUTAN VE PILOT, NORMAL 
CALISMALARIN YANI SIRA, BIR COK SEYLE DE UGRASTILAR. BUNLAR 
UZAY TUTMASI, RADYO ARIZALARI , TIKANMIS TUVALET , 
LUMBUZLARDAKI KIRAGI , ARIZALI RADAR EKRANI VE UYKUSUZLUKTU . 
FAKAT HERSEYE KARSIN, COK BASARILI BIR SEYIRDI . ASTRONOTLAR, 
GEMININ SADECE BIR YUZUNU DAIMA GUNES'E CEVIREREK BIRKAC 
SAAT ISITTILAR, DOGAL OLARAK DIGER TARAF DA DONDU. BOYLECE 



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GEMININ ISISAL OZELLIKLERI SAPTANMIS OLDU . MEKANIK KOLA 
YERLESTIRILEN BIR CIHAZLA, UZAY GEMISI CEVRESINDEKI 
PARCACIKLAR VE ELEKTRIK ALANLARI OLCULDU . MEKANIK KOLUN 
HAREKETINI SUREKLI DENETIM ALTINDA TUTMAK ICIN KOL UZERINE 
YERLESTIRILEN TELEVIZYON KAMERASI ARIZALANINCA, PERSONEL 
AYNI I SI YAPABILMEK ICIN BILDIGIMIZ AVCI DURBUNU KULLANMAK 
ZORUNDA KALDILAR. ILK UCUS GUNUNUN SONUNDA, YERYUZU'NDEN 
HAVALANIRKEN LUMBUZ KORUYUCUSUNU KIRAN BEYAZ MADDENIN , 
GEMININ BAS KISMINDAN KOPAN ISI KORUYUCU OLDUGUNU 
KESFETTILER. PERSONEL ILK GUN HICBIR SEY YIYEMEDI . AYRICA 
PILOT, AGIRLIKSIZ ORTAMA ALISAMADIGINDAN UYUYAMADI ; 
DOLAYISIYLA DA IKINCI GUN COK YORGUN DUSMUSTU. BU DURUMU 
PILOT SU SOZLERLE DILE GETIRIYORDU: "KENDIMI , SANKI HER ON 
DAKIKADA BIR MARATON KOSUYORMUS GIBI HISSETTIM." BU SEYIRDE 
AYRICA ARl, PERVANE, VE , SINEKLERDEN OLUSAN HAYVANLARIN , 
AGIRLIKSIZ ORTAMDA DAVRANISLARI INCELENDI . ARILAR UCMAKTAN 
YORULDUKLARINDA , AMACSIZ BIR SEKILDE OLDUKLARI YERE 
DONUYORLARDI . GEMI DUNYA ' YA DONDUGUNDE TUM ARILAR OLMUSTU. 
PERVANELER CILGIN BIR SEKILDE KANAT CIRPTILAR; SINEKLER HEP 
YURUDULER. PILOT UCMAK ICIN CALISAN BIR SINEGI ASLA 
GORMEDIGINI SOYLUYORDU. INISIN YAPILACAGI EDWARDS HAVA 
KUVVETLERI USSU'NDEKI KURU GOL YATAGI MEVSIMIN DE ETKISIYLE 
INIS GUNU lYICE ISLANMISTI. BU NEDENLE , INIS ORAYA DEGIL DE , 
NEW MEXICO 'DAKI LIMANA YAPILDI . FAKAT INISIN YAPILACAGI GUN 
KUVVETLI BIR FIRTINA PATLAMIS VE INISIN YAPILACAGI ALAN, 
SEYIRDEKI GEMIDEN DAHI RAHATCA GORULEBILEN BEYAZ BIR TOZ 
BULUTU ALTINDA KALMISTI. BU NEDENLE UCUS BIR GUN 
GECIKTIRILDI. DORDUNCU UCUS, 27 HAZIRAN- 4 TEMMUZ 1982 ARASI 
GERCEKLESTIRILDI. BU SEYIR DIGERLERINDEN IKI YONDEN 
FARKLIYDI. BIRINCISI, ASKERI AMACLI YUK TASIYORDU. HAVA 
KUVVETLERI YUKUN NE OLDUGUNU ACIKLAMADI . FAKAT BU GIZLI 
YUKUN, KIRMIZIOTESI ARAMA VE TARAMA YAPAN BIR ALET OLDUGU 
BILINIYORDU. IKINCI FARKLI YON, OGRENCILERIN HAZIRLADIGI 90 
KG. AGIRLIGINDAKI DENEY PAKETININ TASINMASIYDI . BU SEYIRDE 



78 



YAPILAN BIR BASKA DENEY DE BAZI BIYOLOJIK- MATERYALIN 
BIRBIRLERINDEN AYRILMASIYDI . DENEYI YAPAN ALET , BU MATERYAL 
KARISIMI BIR ELEKTRIK ALANA KOYUYOR VE ONLARI DOGAL ELEKTRIK 
YUKLERINE GORE SECEBILIYORDU . DUNYA USTUNDE BU ISLEMI, 
YERCEKIMI ETKILEMEKTE ELEKTRIK YUKU , SICAKLIK VE CALKANTIYA 
NEDEN OLMAKTA, DOLAYISIYLA DA MATERYAL TEKRAR BIRBIRINE 
KARISMAKTADIR. UZAYDA BU MATERYALLERI BIRBIRINDEN AYIRMANIN, 
800 KEZ DAHA ETKIN OLDUGU ORTAYA CIKARILDI . BU SON DENEME 
UCUSUYDU. BUNDAN SONRAKI UCUSLAR, NORMAL TICARI AMACLI 
OLACAKTI. DORDUNCU UCUSTA BASARIYA ULASAMIYAN EN ONEMLI 
NOKTA, KATI YAKITLI ROKETLERIN PARASUT MEKANIZMASININ 
ARIZALANMASI VE HER BIRI 7 MILYAR TL ' NA MAL OLAN BU 
ROKETLERIN DENIZ DIBINI BOYLAMASIYDI . BESINCI UCUSUN 
PERSONEL SAYISI, ILK KEZ IKIDEN FAZLA OLUYORDU . UCUS 
KOMUTANI VE PILOTTAN BASKA, WILLIAM VE JOSEPH ADLI IKI 
ASTRONOT DA UCUS UZMANI OLARAK GEMIDE YER ALDILAR. GEMININ 
ILK TICARI YUKU OLAN ILETISIM UYDULARI II KASIM 1982 GUNU 
BASLAYAN BU SEFERDE BASARIYLA YORUNGEYE OTURTULDU . EGER BU 
UYDULAR YERDEN YORUNGEYE YERLESTIRILSEYDI , UYDU SAHIPLERI 
DAHA FAZLA PARA ODEMEK ZORUNDA KALACAKLARDI . BU SEYIRDE 
PERSONELI UZAY TUTTU. BU YUZDEN UZAYDA YURUYUS IZLENCESI BIR 
GUN ERTELENDI. ERTESI GUN ISE HER BIRI YARIM MILYAR TL ' NA 
MAL OLAN UZAY MELBUSATI ARIZALANDI . TUM UGRASLARA KARSIN 
ARIZALAR GIDERILEMEDIGI ICIN YURUYUSTEN VAZGECILDI . FAKAT BU 
COK ONEMLI BIR DENEYDI ; CUNKI GELECEKTE UZAY LIMANI GIBI 
BUYUK YAPILAR INSA EDILIRKEN, BU TECHIZAT ILE ARAC DISI 
CALISMALAR YAPILACAK. 



79 



B. PROGRAMS 

Two programs are used to find the frequencies of the 
symbols in the magazine articles given above. A Fortran 
program creates a data set format which can be processed by 
SAS program. The program which sets the logical record 
length of data file to 1, is given below. 

//SUHAl JOB (2979,5555) , 'SUHA' ,CLASS=A 

//"MAIN ORG=NPGVM1.297 9P 

// EXEC FORTVCG 

//FORT. SYS IN DD " 

C THIS PROGRAM CONVERTS ONE LOGICAL RECORD OF 

C EIGHTY CHARACTERS TO EIGHTY 

C LOGICAL RECORDS OF ONE CHARACTER EACH. 

C 

C UNIT 5: INPUT 

C UNIT 1: OUTPUT 



C 



DIMENSION A(80) 

LINES = 
10 CONTINUE 

READ(5,20,END=100) A 
20 FORMAT(80A1) 

LINES = LINES + 1 

DO 30 1=1,80 

WRITE(1,20) A(I) 
30 CONTINUE 

GO TO 10 
100 CONTINUE 

WRITE (6, 110) LINES 
110 FORMAT ( IX ,' NUMBER OF LINES READ: ',17) 

STOP 

END 



/" 



80 



//GO.FTOIFOOI DD UNIT=3350 , VOL=SER=MVS004 , 
DISP= (NEW, KEEP) , 

// DCB= (RECFM=FB,LRECL=1,BLKSIZE=6000) , 
// SPACE=(TRK, (1,1)) ,DSN=S297 9.LETTER 
//GO. SYS IN DD " 

Insert text here. (Also, remove this line) 

// 



81 



The second program is run to count the frequency of each 
type of letter. This SAS program is given below. 

//SUHA4 JOB (2979,5555) , 'SUHA' ,CLASS = B 

//"MAIN ORG=NPGVM1.29 7 9P 

// EXEC SAS 

//TEXT DD UNIT=3350,VOL=SER=MVS004,DISP=SHR, 

DSN=S2979.ALPHA1 

//SYS IN DD '- 

OPTIONS LINESIZE = 80; 

DATA TEXT; 

INFILE TEXT; 

INPUT (§1 LETTER $CHAR1. ; 

IF LETTER EQ ' ' THEN DELETE; 
PROG FREQ DATA=TEXT; 

TABLES LETTER; 
I- 
II 

//SUHA4 JOB (2979,5555) , 'SUHA' ,CLASS=B 
//"MAIN ORG=NPGVM1.29 7 9P 
// EXEC SAS 

//TEXT DD UNIT=3350,VOL=SER=MVS004,DISP=SHR, 
DSN=S2979.ALPHA1 
//SYSIN DD " 
OPTIONS LINESIZE =80; 
DATA TEXT; 

INFILE TEXT; 

INPUT (§1 LETTER $CHAR1. ; 

IF LETTER EQ ' ' THEN DELETE; 
PROC FREQ DATA=TEXT; 

TABLES LETTER; 
/" 
// 



82 



APPENDIX B 
THE LISP PROGRAM OF CODING PROCESS 

(defun huffman (P) 

(sortcar (assign (arrange (mapcar 'list P))) 'greaterp)) 

(defun arrange (Q) 

(cond ((null (cdr Q) ) Q) 

(t (arrange (insert (list (add (caar Q) (caadr Q) ) 

(car Q) (cadr Q) ) 
(cddr Q)) )) )) 

(defun insert (x Q) 

(cond ((null Q) (cons x Q)) 

((lessp (plus (car x) E) (caar Q)) (putin N x Q)) 
(t (cons (car Q) (insert x (cdr Q)) )) )) 

(defun putin (n x L) 

(cond ((zerop n) (cons x L)) 
((null L) (list x)) 
(t (cons (car L) (putin (subl n) x (cdr L)))))) 

(defun assign (Q) (split nil (car Q) ) ) 

(defun split (c L) 

(cond ((null (cdr L)) (list (list (car L) c)) ) 
(t (append (split (cons 1 c) (cadr L)) 

(split (cons c) (caddr L)) )) )) 

(defun sortcode (L) 
(cond ((null L) nil) 
(t (inscode (caar L) (cadar L) (sortcode (cdr L)) )) )) 

(defun inscode (p c L) 

(cond ((null L) (list (list p c)) ) 
((greaterp (length c) (length (cadar L))) 



83 



(cgns (list p (cadar L)) (inscode (caar L) c (cdr L)) )) 
(t (cons (list p c) L)) )) 

(defun totlength (L) 
(cond ((null L) 0) 

(t (add (times (caar L) (length (cadar L)) ) 
(totlength (cdr L) ) )) )) 

(defun avglength (L) 

(quotient (times 1.0 (totlength L)) 

(apply 'add (mapcar 'car L)) )) 

(defun varlength (L) 

(quotient (times 1.0 (varlength2 L (avglength L))) 
(apply 'add (mapcar 'car L)))) 

(defun varlength2 (L mu ) 
(cond ((null L) 0) 

(t (add (times (caar L) 

(expt (difference (length (cadar L)) mu) 2)) 
(varlength2 (cdr L) mu))))) 

(defun Zipf (n) 

(cond ((zerop n) nil) 

(t (cons (quotient 1.0 n) (Zipf (- n 1)) )) )) 

(defun tryN (n e) 
(set 'N n) 
(set 'E e) 

(set 'code (sortcode (huffman Turkish)) ) 
(print (list 'N '= n 'E '= e)) 
(pp code) 

(print (list 'mean '= (avglength code))) (terpr) 
(print (list 'variance ' = (varlength code))) (terpr)) 

(set 'Turkish 
'(0.0 0.00006 0.00006 0.00017 0.00028 0.00034 
0.00039 0.00045 0.00045 0.00056 0.00061 0.00067 



84 



0.00067 0.00073 0.00073 0.00084 0.00084 0.00089 

0.00112 0.00134 0.00162 0.00196 0.00358 0.00581 

0.00687 0.00872 0.00989 0.01017 0.01224 0.01637 

0.01883 0.02185 0.02660 0.02682 0.02945 0.03213 

0.03509 0.03861 0.03984 0.05130 0.05163 0.06085 

0.06611 0.07952 0.09427 0.10528 0.13339)) 

(set 'N 0) 
(set 'E 0) 



85 



APPENDIX C 
THE SAS POGRAM USED FOR FINDING THE BUFFER SIZE 

//SUHA6 JOB (2979,5555) , 'SUHA' ,CLASS=B 

//"MAIN ORG=NPGVM1.2979P 

// EXEC SAS 

//DATAIN DD UNIT=3350 , VOL=SER=MVS004 ,DISP=SHR,DSN=S2979 . ALPHAl 

//SYSIN DD " 

DATA ONE; 

INFILE DATAIN; 

INPUT LETTER $ 1; 
DATA ONE; 

SET ONE; 



For each letter, assign its number of bits 
in the used code. 



IF 


LETTER 


EQ 


'/ 


THEN 


BITS 


— 


IF 


LETTER 


EQ 


'I' 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'A 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'E 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'N 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'R 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'U 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'L 


THEN 


BITS 


- 


IF 


LETTER 


EQ 


'S 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'K 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'P 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


' T 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'M 


THEN 


BITS 


= 


IF 


LETTER 


EQ 


'Y 


THEN 


BITS 


- 


IF 


LETTER 


EQ 


'0 


' THEN 


BITS 


- 


IF 


LETTER 


EQ 


'G 


' THEN 


BITS 


= 


IF 


LETTER 


EQ 


'B 


' THEN 


BITS 


= 



86 



IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
IF LETTER EQ 
DATA ONE; 



'C 


THEN 


BITS 


1 T 
5 


THEN 


BITS 


t t 


THEN 


BITS 


'Z' 


THEN 


BITS 


'V 


THEN 


BITS 


'P' 


THEN 


BITS 


'H' 


THEN 


BITS 


•f' 


THEN 


BITS 


'0' 


THEN 


BITS 


I I T 


' THEN BITS 


'1' 


THEN 


BITS 


t ft I 


THEN 


BITS 


'2' 


THEN 


BITS 


')' 


THEN 


BITS 


'5' 


THEN 


BITS 


'3' 


THEN 


BITS 


'8' 


THEN 


BITS 


'(' 


THEN 


BITS 


'4' 


THEN 


BITS 


I . r 

> 


THEN 


BITS 


'9' 


THEN 


BITS 


'J' 


THEN 


BITS 


'6' 


THEN 


BITS 


'W 


THEN 


BITS 


' . ' 


THEN 


BITS 


'7' 


THEN 


BITS 


T I 


THEN 


BITS 


' ? ' 


THEN 


BITS 


'X' 


THEN 


BITS 


'Q' 


THEN 


BITS 



Let RATE = Output capacity of the processor in 
bits per unit time. 



87 



SET ONE; 

RATE = 4.30771; 

BUFFER + BITS; 

BUFFER = BUFFER - RATE; 

IF BUFFER LE THEN BUFFER = 0; 
OPTIONS LINESIZE =80; 
PROG FREQ DATA=ONE; 

TABLES BUFFER; 
PROC MEANS DATA=ONE MEAN STD MIN MAX; 

VAR BUFFER; 
/" 
// 



88 



LIST OF REFERENCES 



1. Hamming R.W., Coding and Information Theory, 
Prentice-Hall, Inc., 1980. 

2. Huffman, D. , "A Method for the Construction of Minimum 
Redundancy Codes". Proceedings of the Institude of 
Radio Engineers, Vol. 40 , pp . Ta98^TT0Tr; September 

3. Stegers Wolfgang, ceviren Hataysal H. "Modern 
Gemilerin Garip Bicimleri" , Bilim ve Teknik, Cilt 16, 
Sayi 191, Ekim 1983. 

4. Dr. Derman I. Ethem, "Uzay Mekigi'nin Oykusu" , Bilim 
ve Teknik, Cilt 17, Sayi 194, Ocak 1984. 

5. SAS Institude Inc. SAS User's Guide: Basics 1982 
Edition , Cary NC : SAS Institude Inc., 1982 

6. Foderaro John K., The FRANZ LISP Manual, Universty of 
California, 1980 

7. Winston Patrick Henry, Horn Berthold Klaus Paul, LISP, 
1984 



89 



INITIAL DISTRIBUTION LIST 



No. Copies 



1. Defense Technical Information Center 2 
Cameron Station 

Alexandria, Virginia 22314 

2. Library, Code 0142 2 
Naval Postgraduate School 

Monterey, California 93943 

3. Department Chairman, Administrative Science 1 
Code 54Gk 

Department of Administrative Science 
Naval Postgraduate School 
Monterey, California 93943 

4. Department Chairman, Computer Science 1 
Code 52MI 

Department of Computer Science 
Naval Postgraduate School 
Monterey, California 93943 

5. Prof. Hamming R.W., Code 52Hg 2 
DEpartment or Computer Science 

Naval Postgraduate School 
Monterey, California 93943 

6. Prof. Daniel R. Dolk, Code 54Dk 1 
Department of Administrative Science 

Naval Postgraduate School 
Monterey, California 93943 

7. Ibrahim KiliQ 1 
Bulbulderesi Cad. No = 42/7 

Kucukesat, Ankara TURKEY 

8. Dz. K. Komutanligi 5 
Personel Daire B§k.ligi 

Bakanliklar, Ankara TURKEY 

9. Dz. Harb Okulu K.ligi 1' 
Fen Bilimleri Bl. Bsk.ligi 

Heybeliada, Istanbul TURKEY 

10. Deniz Harb Okulu K.ligi 1 
Kutuphanesi 

Heybeliada, Istanbul TURKEY 

11. Istanbul Teknik Universtesi 1 
Kutuphanesi 

Istanbul, TURKEY 

12. Bogazigi Universtesi 1 
Kutuphanesi 

Istanbul, TURKEY 

13. Orta Dogu Teknik Universtesi 1 
Kutuphanesi 

Ankara , TURKEY 



90 



14. Suha Kilic 

Bulbulderesi Cad. No - 42/7 
Kucukesat, Ankara TURKEY 



91 



13.37 5 




211S35 



Thesis 

KiH12 KiliQ 

c.l Modification of Huff- 



man Coding. 




8 OCT 8<? 
14 JUL 67 



4 



3 33 68 

3 35 1 3 



ft 



211S35 



Thesis 

KUi12 Kilig 

c.l Modification of Huff- 
man Coding.