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

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2 Author(s)
Faraji-Dana, Z. ; Dept. of Med. Biophys., Univ. of Toronto, Toronto, ON, Canada ; Mitran, P.

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, mathbb{F}, and adopt a non-binary PSK modulation. The relay then directly decodes the network-coded combination {aS_A+bS_B} over mathbb{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 mathbb{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.

Published in:

Wireless Communications, IEEE Transactions on  (Volume:12 ,  Issue: 1 )