Coding and System Design for Quantize-Map-and-Forward Relaying

TL;DR

This paper introduces a low-complexity coding and system design framework for half-duplex relay channels using Quantize-Map-and-Forward, employing LDPC and LDGM codes with belief propagation decoding, achieving near-optimal performance.

Contribution

It presents a novel low-complexity coding scheme for QMF relay channels, integrating LDPC and LDGM codes with belief propagation, and extends to high SNR with BICM, matching theoretical limits.

Findings

Codes perform within 1dB of QMF threshold

Belief propagation effectively decodes joint signals

Framework scalable to high SNR regimes

Abstract

In this paper we develop a low-complexity coding scheme and system design framework for the half duplex relay channel based on the Quantize-Map-and-Forward (QMF) relay- ing scheme. The proposed framework allows linear complexity operations at all network terminals. We propose the use of binary LDPC codes for encoding at the source and LDGM codes for mapping at the relay. We express joint decoding at the destination as a belief propagation algorithm over a factor graph. This graph has the LDPC and LDGM codes as subgraphs connected via probabilistic constraints that model the QMF relay operations. We show that this coding framework extends naturally to the high SNR regime using bit interleaved coded modulation (BICM). We develop density evolution analysis tools for this factor graph and demonstrate the design of practical codes for the half-duplex relay channel that perform within 1dB of information theoretic QMF threshold.