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We address in this paper decoding aspects of the Compute-and-Forward (CF)physical-layer network coding strategy. It is known that the original decoderfor the CF is asymptotically optimal. However, its performance gap to optimaldecoders in practical settings are still not known. In this work, we developand assess the performance of novel decoding algorithms for the CF operating inthe multiple access channel. For the fading channel, we analyze the ML decoderand develop a novel diophantine approximation-based decoding algorithm showednumerically to outperform the original CF decoder. For the Gaussian channel, weinvestigate the maximum a posteriori (MAP) decoder. We derive a novel MAPdecoding metric and develop practical decoding algorithms proved numerically tooutperform the original one.

Efficient Decoding Algorithms for the Compute-and-Forward Strategy