Zero-error stationary coding over stationary channels. (English) Zbl 0444.94007

Kieffer, John C.

Z. Wahrscheinlichkeitstheor. Verw. Geb. 56, 113-126 (1981).

Summary: For a type of stationary ergodic discrete-time finite-alphabet channel more general than the stationary totally ergodic \(\bar d\)-continuous channel of Gray, Ornstein and Dobrushin, it is shown that a stationary ergodic source with entropy less than capacity can be transmitted over the channel with zero probability of error using stationary codes for encoding and decoding. This result generalizes the result of R. M. Gray, D. S. Ornstein and R. L. Dobrushin [Ann. Probab. 8, 639–674 (1980; Zbl 0453.94010)] that Bernoulli sources can be transmitted with zero error at rates below capacity over a totally ergodic \(\bar d\)-continuous channel.

Reviewer: John C. Kieffer (Rolla, MO)

MSC:

94A40	Channel models (including quantum) in information and communication theory
94A29	Source coding

Keywords:

stationary ergodic discrete-time finite-alphabet channel; stationary ergodic source; stationary codes

Citations:

Zbl 0453.94010

References:

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