On the BCJR Algorithm for Asynchronous Physical-layer Network Coding

TL;DR

This paper develops a general BCJR-based decoding algorithm for asynchronous physical-layer network coding in bi-directional relaying, accommodating arbitrary pulse-shaping and enabling efficient decoding in practical asynchronous MAC channels.

Contribution

It introduces a general channel model for asynchronous MAC with arbitrary pulse-shaping and develops a BCJR-based optimal decoding algorithm adaptable to low-complexity variants.

Findings

The BCJR algorithm achieves optimal decoding performance for asynchronous MAC.

The framework supports various low-complexity decoding algorithms like Log-MAP and Max-Log-MAP.

The model generalizes previous approaches to arbitrary pulse-shaping in asynchronous channels.

Abstract

In practical asynchronous bi-directional relaying, symbols transmitted by two source nodes cannot arrive at the relay with perfect symbol alignment and the symbol-asynchronous multiple-access channel (MAC) should be seriously considered. Recently, Lu et al. proposed a Tanner-graph representation of symbol-asynchronous MAC with rectangular-pulse shaping and further developed the message-passing algorithm for optimal decoding of the asynchronous physical-layer network coding. In this paper, we present a general channel model for the asynchronous multiple-access channel with arbitrary pulse-shaping. Then, the Bahl, Cocke, Jelinek, and Raviv (BCJR) algorithm is developed for optimal decoding of asynchronous MAC channel. This formulation can be well employed to develop various low-complexity algorithms, such as Log-MAP algorithm, Max-Log-MAP algorithm, which are favorable in practice.