Sequential operation of communication channels and the capacity using variable-length codes
Abstract
We develop a mathematical theory of sequential operation of communication channels, and prove the coding theorem for the capacity using variable-length codes. The mathematical theory consists in constructing the sequential transfer probability function of a continuous-time 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 variable-length codes is then given in terms of this probability function. The coding theorem for the capacity is established by first proving the information-stability theorem using a generalized ergodic theorem. It is shown that for some common channels the capacity using variable-length codes is numerically equal to the ordinary capacity using fixed-length codes.
- Publication:
-
SIAM Journal of Applied Mathematics
- Pub Date:
- July 1978
- Bibcode:
- 1978SJAM...35...31K
- Keywords:
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- 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