A new achievable rate region for the discrete memoryless multiple-access channel with feedback

A single-letter achievable rate region for the two-user discrete memoryless multiple-access channel is proposed. The rate region includes the Cover-Leung region, and it is shown that the inclusion is strict. The proof uses a block-Markov superposition strategy based on the observation that the messages of the two users are correlated given the feedback. The rates of transmission are too high for each encoder to decode the other's message directly using the feedback, so they transmit correlated information in the next block in order to learn the message of one another. They then cooperate in the following block to resolve the residual uncertainty of the decoder. Our scheme may be viewed as a natural generalization of the Cover-Leung scheme with a delay of one extra block and a pair of additional auxiliary random variables. The scheme can also be extended to obtain larger rate-regions with more auxiliary random variables.