A New Achievable Rate Region for the Discrete Memoryless Multiple-Access Channel with Noiseless Feedback

TL;DR

This paper introduces a new achievable rate region for the two-user discrete memoryless MAC with noiseless feedback, surpassing the Cover-Leung region by employing a block-Markov superposition strategy that leverages message correlation.

Contribution

It presents a novel single-letter rate region that extends the Cover-Leung scheme with additional auxiliary variables and a delay, improving achievable rates for the MAC with feedback.

Findings

The new rate region strictly includes the Cover-Leung region.

The scheme is demonstrated on two different MACs, showing improved performance.

Extension to larger rate regions with more auxiliary variables is possible.

Abstract

A new single-letter achievable rate region is proposed for the two-user discrete memoryless multiple-access channel(MAC) with noiseless feedback. The proposed region includes the Cover-Leung rate region [1], 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 to learn the message of one another. They then cooperate in the following block to resolve the residual uncertainty of the decoder. The coding 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. We compute the proposed rate region for two different MACs and compare the results with other known rate regions for the MAC with feedback. Finally, we show how the coding scheme can be extended to obtain larger rate regions with more auxiliary random variables.