Compute--Forward Multiple Access (CFMA): Practical Code Design

TL;DR

This paper introduces a practical compute-forward multiple access strategy using standard LDPC codes and low-complexity decoding to achieve capacity points on the multiple access channel without rate-splitting or time sharing.

Contribution

It demonstrates a practical, low-complexity coding and decoding scheme based on CFMA that attains the dominant face of the MAC capacity with off-the-shelf LDPC codes.

Findings

Achieves within 1.7 dB of theoretical limits.

Uses a two-stage decoding process with sum-product algorithm.

Does not require rate-splitting or time sharing.

Abstract

We present a practical strategy that aims to attain rate points on the dominant face of the multiple access channel capacity using a standard low complexity decoder. This technique is built upon recent theoretical developments of Zhu and Gastpar on compute-forward multiple access (CFMA) which achieves the capacity of the multiple access channel using a sequential decoder. We illustrate this strategy with off-the-shelf LDPC codes. In the first stage of decoding, the receiver first recovers a linear combination of the transmitted codewords using the sum-product algorithm (SPA). In the second stage, by using the recovered sum-of-codewords as side information, the receiver recovers one of the two codewords using a modified SPA, ultimately recovering both codewords. The main benefit of recovering the sum-of-codewords instead of the codeword itself is that it allows to attain points on the dominant face of the multiple access channel capacity without the need of rate-splitting or time sharing while maintaining a low complexity in the order of a standard point-to-point decoder. This property is also shown to be crucial for some applications, e.g., interference channels. For all the simulations with single-layer binary codes, our proposed practical strategy is shown to be within \SI{1.7}{\decibel} of the theoretical limits, without explicit optimization on the off-the-self LDPC codes.