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Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels

R. M. Gray, D. S. Ornstein and R. L. Dobrushin
The Annals of Probability
Vol. 8, No. 4 (Aug., 1980), pp. 639-674
Stable URL: http://www.jstor.org/stable/2242818
Page Count: 36
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Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels
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Abstract

Results are obtained on synchronizing block codes for discrete stationary totally ergodic $\bar{d}$-continuous noisy channels (which may have infinite memory and anticipation) and used to prove sliding-block joint source and channel coding theorems. The coding theorems are used to demonstrate the existence of invulnerable sources--ergodic sources which can be input directly to the channel without encoding and decoded at the receiver with zero error--at all entropy rates below channel capacity. Combining the invulnerable source theorem with the isomorphism theorem of ergodic theory shows that, if the source is a $B$-process with entropy below capacity, then infinite length codes with zero error exist, proving that the zero-error capacity equals the usual channel capacity.

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