Soft-Decoding-Based Strategies for Relay and Interference Channels: Analysis and Achievable Rates Using LDPC Codes

TL;DR

This paper rigorously analyzes soft decoding strategies for relay and interference channels using LDPC codes, providing asymptotic bounds and demonstrating the limitations of certain coding strategies in these contexts.

Contribution

It introduces simultaneous density evolution for soft-DF and adapts iterative detection techniques for soft-IC, offering new theoretical insights into their performance and limitations.

Findings

Soft-DF bounds the decoding error probability at the destination.

Wyner-Ziv coding enhances relay communication in soft-DF.

Optimal point-to-point codes are ineffective for soft-IC and partial decoding strategies.

Abstract

We provide a rigorous mathematical analysis of two communication strategies: soft decode-and-forward (soft-DF) for relay channels, and soft partial interference-cancelation (soft-IC) for interference channels. Both strategies involve soft estimation, which assists the decoding process. We consider LDPC codes, not because of their practical benefits, but because of their analytic tractability, which enables an asymptotic analysis similar to random coding methods of information theory. Unlike some works on the closely-related demodulate-and-forward, we assume non-memoryless, code-structure-aware estimation. With soft-DF, we develop {\it simultaneous density evolution} to bound the decoding error probability at the destination. This result applies to erasure relay channels. In one variant of soft-DF, the relay applies Wyner-Ziv coding to enhance its communication with the destination, borrowing from compress-and-forward. To analyze soft-IC, we adapt existing techniques for iterative multiuser detection, and focus on binary-input additive white Gaussian noise (BIAWGN) interference channels. We prove that optimal point-to-point codes are unsuitable for soft-IC, as well as for all strategies that apply partial decoding to improve upon single-user detection (SUD) and multiuser detection (MUD), including Han-Kobayashi (HK).