Multiplexing Zero-Error and Rare-Error Communications over a Noisy Channel with Feedback

Two independent data streams the "zero-error stream" and the "rare-error stream" are to he 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.