On Non-Binary Constellations for Channel-Coded Physical-Layer Network Coding

Zahra Faraji-Dana

doi:10.1109/TWC.2012.120312.120469

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On Non-Binary Constellations for Channel-Coded Physical-Layer Network Coding

2013-01-01

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Zahra Faraji-Dana *

Patrick Mitran

DOI：10.1109/TWC.2012.120312.120469

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Abstract

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We investigate channel-coded physical-layer network coding in a two-way relaying scenario, where the end nodes A and B choose their symbols, S-A and S-B, from a small non-binary field, F, and adopt a non-binary PSK modulation. The relay then directly decodes the network-coded combination aS(A) + bS(B) over F from the noisy received superimposed channel-encoded packets. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients (a, b). As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of (a, b). In this paper, we compare different mappings between F and the PSK constellation, and prove that many have identical performance in terms of frame error rate (FER). Moreover, we derive a lower bound on the performance of decoding the network-coded combinations. Simulation results show that if we adopt either i) concatenated Reed-Solomon and convolutional coding or ii) low-density parity check codes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the FER and, in particular, the ternary constellation has the best FER performance among all considered cases.

Keywords:

Physical-layer network coding

non-binary constellation mappers

outage probability

Reed Solomon Convolutional code concatenation

low density parity check code

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