The Annals of Probability

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

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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.

Article information

Source
Ann. Probab., Volume 8, Number 4 (1980), 639-674.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994658

Digital Object Identifier
doi:10.1214/aop/1176994658

Mathematical Reviews number (MathSciNet)
MR577308

Zentralblatt MATH identifier
0453.94010

JSTOR
links.jstor.org

Subjects
Primary: 94A15: Information theory, general [See also 62B10, 81P94]
Secondary: 60G10: Stationary processes 28A65 94A05: Communication theory [See also 60G35, 90B18]

Keywords
Coding for noisy channels synchronization sliding-block codes zero error codes information theory

Citation

Gray, R. M.; Ornstein, D. S.; Dobrushin, R. L. Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels. Ann. Probab. 8 (1980), no. 4, 639--674. doi:10.1214/aop/1176994658. https://projecteuclid.org/euclid.aop/1176994658


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