Joint LDPC and Physical-layer Network Coding for Asynchronous Bi-directional Relaying

TL;DR

This paper develops a comprehensive decoding framework for asynchronous bi-directional relaying using LDPC and cyclic codes, addressing practical synchronization issues in physical-layer network coding with improved algorithms and simulation validation.

Contribution

It introduces a general channel model for asynchronous MAC with arbitrary pulse-shaping and proposes a BCJR-based decoding algorithm along with cyclic coding techniques for frame synchronization.

Findings

The BCJR algorithm achieves optimal decoding performance.

Cyclic codes effectively mitigate frame asynchronism.

Simulation results confirm the proposed methods' effectiveness.

Abstract

In practical asynchronous bi-directional relaying, symbols transmitted by two sources cannot arrive at the relay with perfect frame and symbol alignments and the asynchronous multiple-access channel (MAC) should be seriously considered. Recently, Lu et al. proposed a Tanner-graph representation of the symbol-asynchronous MAC with rectangular-pulse shaping and further developed the message-passing algorithm for optimal decoding of the symbol-asynchronous physical-layer network coding. In this paper, we present a general channel model for the asynchronous MAC with arbitrary pulse-shaping. Then, the Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm is developed for optimal decoding of the asynchronous MAC channel. For Low-Density Parity-Check (LDPC)-coded BPSK signalling over the symbol-asynchronous MAC, we present a formal log-domain generalized sum-product-algorithm (Log-G-SPA) for efficient decoding. Furthermore, we propose to use cyclic codes for combating the frame-asynchronism and the resolution of the relative delay inherent in this approach can be achieved by employing the simple cyclic-redundancy-check (CRC) coding technique. Simulation results demonstrate the effectiveness of the proposed approach.