Convolutional Codes in Two-Way Relay Networks with Physical-Layer Network Coding

We study the application of convolutional codes to two-way relay networks (TWRNs) with physical-layer network coding (PNC). When a relay node decodes coded signals transmitted by two source nodes simultaneously, we show that the Viterbi algorithm (VA) can be used by approximating the maximum likelihood (ML) decoding for XORed messages as two-user decoding. In this setup, for given memory length constraint, the two source nodes can choose the same convolutional code that has the largest free distance in order to maximize the performance. Motivated from the fact that the relay node only needs to decode XORed messages, a low complexity decoding scheme is proposed using a reduced-state trellis. We show that the reduced-state decoding can achieve the same diversity gain as the full-state decoding for fading channels.

I. Introduction

IT is known that due to the broadcast nature of wireless channels, it can be useful to perform network coding [1] in the physical layer. Physical-layer network coding (PNC) was proposed by Zhang et al. [2] as a protocol for information exchange between two nodes with the help of a relay in a two-way relay network (TWRN). The information exchange consists of two phases, multiple access (MAC) and broadcast (BC) phases. In the MAC phase, two source nodes simultaneously transmit signals to a relay node. Then, in the BC phase, the relay node broadcasts an XORed codeword, which is encoded from the two source nodes' messages, to two source nodes. It was also reported in [3] that using protocols with two phases in TWRNs can achieve a higher spectral efficiency than using three or four phases. In [4], the notion of PNC was refined and it was demonstrated that how an XORed codeword is obtained by PNC. Note that there could be various ways to represent the XORed codeword, e.g. superimposed XOR was used in [5]. In terms of practical design, there has been extensive research activities on effective modulation and coding schemes for PNC. In [6], when no channel code is considered, an adaptive scheme is proposed to decide detection regions in the MAC phase and to choose a proper constellation in the BC phase. With channel coding, in [7], PNC is performed at message level and the decoding algorithm is redesigned for repeat accumulate (RA) code to decode XORed messages. However, to the best of our knowledge, there is no work studying the use of convolutional coding for PNC yet, where the decoding can be effectively performed by Viterbi algorithm (VA) [8].