Gaussian Multiple Access via Compute-and-Forward

TL;DR

This paper introduces CFMA, a novel multiple-access scheme using compute-and-forward with lattice codes, capable of achieving the entire capacity region for two-user Gaussian MACs at sufficiently high SNRs, and extends to dirty MAC scenarios.

Contribution

It proposes CFMA, a new compute-and-forward based multiple access method that attains full capacity region for two-user MACs without time-sharing, extending to dirty MACs with known interference.

Findings

Achieves entire capacity region for two-user MACs at SNRs above 1+√2.

Extends to dirty MAC with non-causal interference knowledge.

Provides new achievable rate regions for multi-user scenarios.

Abstract

Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC): The receiver successively decodes integer linear combinations of the messages until it can invert and recover all messages. In this paper, a multiple-access technique called CFMA (Compute-Forward Multiple Access) is proposed and analyzed. For the two-user MAC, it is shown that without time-sharing, the entire capacity region can be attained using CFMA with a single-user decoder as soon as the signal-to-noise ratios are above $1+\sqrt{2}$. A partial analysis is given for more than two users. Lastly the strategy is extended to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme extends the previously known results and gives new achievable rate regions.