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.

We establish the deterministic-code capacity region of a network with one transmitter and two receivers: an ordinary receiver and a robust receiver. The channel to the ordinary receiver is a given (known) discrete memoryless channel, whereas the channel to the robust receiver is an arbitrarily varying channel. Both receivers are required to decode the common message (the better-protected message), whereas only the ordinary receiver is required to decode the private message (the less-protected message). As in the single-user case, under the appropriate compactness and convexity conditions, the capacity region is either empty or else the intersection of the capacity regions of the broadcast channels that the various states induce.

To study the fundamental limits on the joint transmission of data of different levels of sensitivity, we establish the deterministic-code capacity region of a network with one transmitter and two receivers: an “ordinary receiver” and a “robust receiver.” The channel to the ordinary receiver is a given (known) discrete memoryless channel, whereas the channel to the robust receiver is an arbitrarily varying channel. Both receivers are required to decode the “common message” (the more sensitive data), whereas only the ordinary receiver is required to decode the “private message” (the less sensitive data).

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.