538 BELL SYSTEM TECHNICAL JOURNAL 



to. A trained operator, however, would say that the sequence sent 

 out by the automatic device was not intelligible. The reason for 

 this is that only a limited number of the possible sequences have been 

 assigned meanings common to him and the sending operator. Thus 

 the number of symbols available to the sending operator at certain 

 of his selections is here limited by psychological rather than physical 

 considerations. Other operators using other codes might make other 

 selections. Hence in estimating the capacity of the physical system 

 to transmit information we should ignore the question of interpretation, 

 make each selection perfectly arbitrary, and base our result on the 

 possibility of the receiver's distinguishing the result of selecting any 

 one symbol from that of selecting any other. By this means the 

 psychological factors and their variations are eliminated and it becomes 

 possible to set up a definite quantitative measure of information 

 based on physical considerations alone. 



Quantitative Expression for Information 



At each selection there are available three possible symbols. Two 

 successive selections make possible 3^, or 9, different permutations or 

 symbol sequences. Similarly n selections make possible 3" different 

 sequences. Suppose that instead of this system, in which three 

 current values are used, one is provided in which any arbitrary number 

 5 of different current values can be applied to the line and distinguished 

 from each other at the receiving end. Then the number of symbols 

 available at each selection is 5 and the number of distinguishable 

 sequences is 5". 



Consider the case of a printing telegraph system of the Baudot 

 type, in which the operator selects letters or other characters each of 

 which when transmitted consists of a sequence of symbols (usually 

 five in number). We may think of the various current values as 

 primary symbols and the various sequences of these which represent 

 characters as secondary symbols. The selection may then be made 

 at the sending end among either primary or secondary symbols. 

 Let the operator select a sequence of n^ characters each made up of 

 a sequence of wi primary selections. At each selection he will have 

 available as many different secondary symbols as there are different 

 sequences that can result from making «i selections from among the 

 5 primary symbols. If we call this number of secondary symbols Si, 

 then 



52 = 5"'. (1) 



For the Baudot System 



52 = 2^ = 32 characters. (2) 



