Compute-forward multiple access (CFMA) with nested LDPC codes

Inspired by the compute-and-forward scheme from Nazer and Gastpar, a novel multiple-access scheme introduced by Zhu and Gastpar makes use of nested lattice codes and sequential decoding of linear combinations of codewords to recover the individual messages. This strategy, coined compute-forward multiple access (CFMA), provably achieves points on the dominant face of the multiple-access capacity region while circumventing the need of time sharing or rate splitting. For a two-user multiple-access channel (MAC), we propose a practical procedure to design suitable codes from off-the-shelf LDPC codes and present a sequential belief propagation decoder with complexity comparable with that of point-to-point decoders. We demonstrate the potential of our strategy by comparing several numerical evaluations with theoretical limits.

I. Introduction

The promise of non-orthogonal multiple-access communication schemes is to operate at rate points beyond the convex combinations of single-user capacities (attained by orthogonal resource sharing) in an attempt to achieve the MAC capacity region. Several encoding and decoding schemes have been proposed in the literature: simultaneous joint decoding, which recovers all messages at once, is optimal in terms of achievable rates but suffers from high complexity; successive cancellation decoding is also first-order optimal but requires time sharing to obtain all rate points on the dominant face; rate splitting as proposed by Rimoldi and Urbanke [1] is also optimal but requires superposition coding and additional decoding steps, which in practical systems may entail some complexity overhead.