Necessary and sufficient conditions are derived for the transmission of two arbitrarily correlated sources over a discrete memoryless asymmetric multiple-access channel. It is shown that in this situation the classical separation principle of Shannon (the factorization of the joint source-channel transmission problem into separate source and channel coding problems) applies. This asymmetric case is the first non-trivial situation of a multiple-access channel with arbitrarily correlated sources in which the sufficient conditions found for the reliable transmission of the sources over the channel turn out to be necessary as well. Furthermore, it is demonstrated that these necessary and sufficient conditions continue to hold if feedback is available to one or both of the encoders.

It is shown that for an asymmetric multiple-access channel, it is possible, starting with one codeword at each of the encoders, to add the codewords for one message at a time (first for the elements in the set of private messages and thereafter for the messages in the set of common messages) and to construct this way, iteratively, a code for this channel with the average error probability upper-bounded by an exponentially small quantity. Using this result, it is subsequently shown that a code for the asymmetric multiple-access channel can also be generated by only. a few (linear in the block length) permutations, still keeping the average error probability upper-bounded by the same error bound and in this way gaining storage space.

An iterative technique is studied for constructing codes for the asymmetric broadcast channel which achieve the exponential error bound of Körner and Sgarro. The codes are generated by a sequence of relatively few (i.e., linear in blocklength) permutations. This technique generalizes and extends earlier results of Ahlswede and Dueck and of the author.

Ahlswede and Dueck introduced an iterative method for constructing codes for the discrete memoryless channel that meet the random coding bound. Their codes are constructed by making a relatively few permutations of a single codeword. In this correspondence their idea is extended to the broadcast channel with degraded message sets. The codes constructed here have average error probabilities below the error bounds derived by Körner and Sgarro.