Multiplexing Zero-Error and Rare-Error Communications Over a Noisy Channel

Abstract

Two independent data streams are to be transmitted over a noisy discrete memoryless channel with noiseless (ideal) feedback. Errors are tolerated only in the second stream, provided that they occur with vanishing probability. The rate of the error-free stream cannot, of course, exceed the channel's zero-error feedback capacity, and nor can the sum of the streams' rates 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 channel behavior-as is needed to achieve zero-error communication-and planning for the typical channel behavior-as is needed to communicate near the Shannon limit-are thus not incompatible. It is further shown that feedback may be beneficial for the multiplexing problem even on channels on which it does not increase the zero-error capacity.