Compute-Forward Multiple Access for Gaussian Fast Fading Channels

TL;DR

This paper extends compute-forward multiple access (CFMA) to Gaussian fast fading channels, developing lattice decoding schemes and analyzing conditions for achieving ergodic sum capacity with only receiver-side channel state information.

Contribution

It introduces lattice decoding for CFMA in fading channels and establishes conditions for achieving ergodic sum capacity with limited channel information.

Findings

Sum capacity is achievable when channel variance is small compared to mean channel strength.

Developed lattice decoding schemes for fading MAC with CFMA.

Derived necessary and sufficient conditions for capacity achievement.

Abstract

Compute-forward multiple access (CFMA) is a transmission strategy which allows the receiver in a multiple access channel (MAC) to first decode linear combinations of the transmitted signals and then solve for individual messages. Compared to existing MAC strategies such as joint decoding or successive interference cancellation (SIC), CFMA was shown to achieve the MAC capacity region for fixed channels under certain signal-to-noise (SNR) conditions without time-sharing using only single-user decoders. This paper studies the CFMA scheme for a two-user Gaussian fast fading MAC with channel state information only available at the receiver (CSIR). We develop appropriate lattice decoding schemes for the fading MAC and derive the achievable rate pairs for decoding linear combinations of codewords with any integer coefficients. We give a sufficient and necessary condition under which the proposed scheme can achieve the ergodic sum capacity. Furthermore, we investigate the impact of channel statistics on the capacity achievability of the CFMA scheme. In general, the sum capacity is achievable if the channel variance is small compared to the mean value of the channel strengths. Various numerical results are presented to illustrate the theoretical findings.