Linear-programming Decoding of Non-binary Linear Codes

Conference: SCC'08 - 7th International ITG Conference on Source and Channel Coding
01/14/2008 - 01/16/2008 at Ulm, Germany

Proceedings: SCC'08

Pages: 6Language: englishTyp: PDF

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Flanagan, Mark F. (Institute for Digital Communications, The University of Edinburgh, Edinburgh EH9 3JL, Scotland)
Skachek, Vitaly; Byrne, Eimear; Greferath, Marcus (Claude Shannon Institute, University College Dublin, Belfield, Dublin 4, Ireland)

We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the ‘maximum likelihood certificate’ property, and we show that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. LP decoding performance is illustrated for the (11, 6, 5) ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the LP decoder performance is comparable to codeword-error-rate-optimum hard-decision based decoding.