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

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.