Translator Disclaimer
August, 1980 Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels
R. M. Gray, D. S. Ornstein, R. L. Dobrushin
Ann. Probab. 8(4): 639-674 (August, 1980). DOI: 10.1214/aop/1176994658

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.

Citation

Download Citation

R. M. Gray. D. S. Ornstein. R. L. Dobrushin. "Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels." Ann. Probab. 8 (4) 639 - 674, August, 1980. https://doi.org/10.1214/aop/1176994658

Information

Published: August, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0453.94010
MathSciNet: MR577308
Digital Object Identifier: 10.1214/aop/1176994658

Subjects:
Primary: 94A15
Secondary: 28A65, 60G10, 94A05

Rights: Copyright © 1980 Institute of Mathematical Statistics

JOURNAL ARTICLE
36 PAGES


SHARE
Vol.8 • No. 4 • August, 1980
Back to Top