Low-Density Graph Codes for slow fading Relay Channels

TL;DR

This paper introduces a new LDPC code structure optimized for slow fading relay channels with coded cooperation, achieving near-outage performance across various block lengths and rates up to 0.5.

Contribution

It extends full-diversity root-LDPC codes to be rate-compatible for cooperative relay channels, enabling improved outage performance.

Findings

Achieves near-outage limit performance for various block lengths.

Supports coding rates up to 0.5, the maximum for two-user cooperation.

Demonstrates full diversity can be maintained with rate constraints.

Abstract

We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-and-forward with a smaller outage probability than the latter. An outage probability analysis for discrete constellations shows that full diversity can be achieved only when the coding rate does not exceed a maximum value that depends on the level of cooperation. We derive a new code structure by extending the previously published full-diversity root-LDPC code, designed for the BF point-to-point channel, to exhibit a rate-compatibility property which is necessary for coded cooperation. We estimate the asymptotic performance through a new density evolution analysis and the word error rate performance is determined for finite length codes. We show that our code construction exhibits near-outage limit performance for all block lengths and for a range of coding rates up to 0.5, which is the highest possible coding rate for two cooperating users.