Sequential operation of communication channels and the capacity using variablelength codes
Abstract
We develop a mathematical theory of sequential operation of communication channels, and prove the coding theorem for the capacity using variablelength codes. The mathematical theory consists in constructing the sequential transfer probability function of a continuoustime channel relative to a stopping rule. It probabilistically describes the sequential output behavior of the channel in response to a given input sequence of functions. The mathematical definition of the capacity using variablelength codes is then given in terms of this probability function. The coding theorem for the capacity is established by first proving the informationstability theorem using a generalized ergodic theorem. It is shown that for some common channels the capacity using variablelength codes is numerically equal to the ordinary capacity using fixedlength codes.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 July 1978
 Bibcode:
 1978SJAM...35...31K
 Keywords:

 Channel Capacity;
 Channels (Data Transmission);
 Coding;
 Communication Theory;
 Probability Theory;
 Sequential Control;
 Algebra;
 Probability Distribution Functions;
 Transfer Functions;
 Transformations (Mathematics);
 White Noise;
 Communications and Radar