Multiplexing zero-error and rare-error communications over a noisy channel with feedback

Abstract

Two independent data streams — the “zero-error stream” and the “rare-error stream” — are to be transmitted over a noisy discrete memoryless channel with feedback. Errors are tolerated only in the rare-error stream, provided that their probability tends to zero. Clearly the rate of the error-free stream cannot exceed the channel's zero-error feedback capacity, and the sum of the streams' rates cannot exceed the channel's Shannon capacity. Using a suitable coding scheme, these necessary conditions are shown to characterize all the achievable rate pairs. Planning for the worst — as is needed to achieve zero-error communication — and planning for the true channel — as is needed to communicate near the Shannon limit — are thus not incompatible.