A Primer on Information Theory 



11 



is useless because the message '1 1 1 IT could be read as 'A E' (11 1 1 1) or 'E A' 

 (111 11). 



R. M. Fano (8) has devised a simple method for establishing a confusion- 

 proof code. It goes as follows: all the categories to be encoded are divided up 

 into two groups; the symbols T and '0' are assigned to these. Each of the 

 two groups is, in turn, subdivided into subgroups; these are designated '1' and 

 '0' in the second digit. The procedure of subdividing is continued until no 

 subgroup contains more than a single category. At any stage of partitioning, 

 the subgroups may contain unequal numbers of categories; accordingly, the 

 number of steps to complete the coding does not have to be the same for all 

 categories. This results in words of unequal length. In spite of this, messages 

 composed of code groups formed according to this rule will be perfectly un- 

 equivocal. 



Fano's method will be illustrated by three ways of making up a code for 

 five categories : 



(a): separate category 'A' from the others in the first step; use two more 

 steps to subdivide the remaining four categories. 



Category 



1st step 



2nd step 



3rd step 



Final code 



A 

 B 

 C 

 D 

 E 



I 





 

 

 



1 

 1 

 

 



1 1 



1 



1 







1 



1 I 



1 



I 







{b) : Use the first step to separate 'A or B' from 'C or D or E' : 

 Category 1st step 2nd step 3rd step Final code 



(c): First step as in {a); the second step is used to separate 'B' from 'C or 

 D or E'; the third separates 'C from 'D or E'; and the fourth separates 'D' 

 from'E': 



r 



