Summary
For a type of stationary ergodic discrete-time finite-alphabet channel more general than the stationary totally ergodic ¯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 Gray et al. [3] that Bernoulli sources can be transmitted with zero error at rates below capacity over a totally ergodic ¯d-continuous channel.
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References
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Research of author supported by NSF Grant MCS-78-21335 and the Joint Services Electronics Program under Contract N00014-79-C-0424.
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Kieffer, J.C. Zero-error stationary coding over stationary channels. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56, 113–126 (1981). https://doi.org/10.1007/BF00531977
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DOI: https://doi.org/10.1007/BF00531977