Channel Coding and Decoding in a Relay System Operated with Physical-Layer Network Coding

This paper investigates link-by-link channel-coded PNC (Physical layer Network Coding), in which a critical process at the relay is to transform the superimposed channel-coded packets received from the two end nodes (plus noise), Y-3 = X-1 + X-2+W-3, to the network-coded combination of the source packets, S-1 circle plus S-2. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain both S-1 and S-2 explicitly at the relay node. Trying to obtain S-1 and S-2 explicitly is an overkill if we are only interested in S-1 circle plus S-2. In this paper, we refer to the transformation Y-3 -> S-1 circle plus S-2 as the Channel-decoding-Network-Coding process (CNC) in that it involves both channel decoding and network coding operations. This paper shows that if we adopt the Repeat Accumulate (RA) channel code at the two end nodes, then there is a compatible decoder at the relay that can perform the transformation Y-3 -> S-1 circle plus S-2 efficiently. Specifically, we redesign the belief propagation decoding algorithm of the RA code for traditional point-to-point channel to suit the need of the PNC multiple-access channel. Simulation results show that our new scheme outperforms the previously proposed schemes significantly in terms of BER without added complexity.