Relay denoising mapping approach designand performance analysis forheterogeneous physical-layer networkcoding with high-order modulation

In recent years, considerable studies have been devoted to physical-layer network coding (PLNC) in a two-way relay channel (TWRC) network with the symmetric channel. However, it may not be appropriate for the asymmetric channel in which the source-to-relay channels are not equally strong and the two sources may utilise different modulation. In this study, the authors studied the heterogeneous PLNC design in the asymmetric TWRC network with high-order modulation and proposed a relay denoising mapping approach to reduce the decoding error probability. Firstly, they put forward a cluster maximisation algorithm to enlarge one cluster by sucking the neighbour points, which satisfy the exclusive law. Then, based on this algorithm, they designed the heuristic nearest-neighbour denoising mapping (HNDM) approach. The HNDM algorithm divides the nearest neighbour superimposed constellation points into the same cluster as far as possible. Points in the same cluster are coded into a new symbol by a specific mapping that achieves a many-to-one mapping. Performance results are provided in terms of symbol error rate. Under diversity channel conditions, the performances of 16-quadrature amplitude modulator (16-QAM)-8-phase-shift keying and 16-QAM-quadrature phase-shift keying are evaluated.