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.
Publié le : 1980-08-14
Classification:
Coding for noisy channels,
synchronization,
sliding-block codes,
zero error codes,
information theory,
94A15,
60G10,
28A65,
94A05
@article{1176994658,
author = {Gray, R. M. and Ornstein, D. S. and Dobrushin, R. L.},
title = {Block Synchronization, Sliding-Block Coding, Invulnerable Sources and Zero Error Codes for Discrete Noisy Channels},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 639-674},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994658}
}
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., Tome 8 (1980) no. 6, pp. 639-674. http://gdmltest.u-ga.fr/item/1176994658/