ML Decoding Via Mixed-Integer Adaptive Linear Programming

    •  Draper, S.C.; Yedidia, J.S.; Wang, Y., "ML Decoding via Mixed-Integer Adaptive Linear Programming", IEEE International Symposium on Information Theory (ISIT), June 2007.
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      • @inproceedings{Draper2007jun1,
      • author = {Draper, S.C. and Yedidia, J.S. and Wang, Y.},
      • title = {ML Decoding via Mixed-Integer Adaptive Linear Programming},
      • booktitle = {IEEE International Symposium on Information Theory (ISIT)},
      • year = 2007,
      • month = jun,
      • url = {}
      • }
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Linear programming (LP) decoding was introduced by Feldman et al. (IEEE Trans. Inform. Theory Mar. 2005) as a novel way to decode binary low-density parity-check codes. Taghavi and Siegel (Proc. ISIT 2006) describe a computationally simplified decoding approach they term "adaptive" LP decoding. Adaptive LP decoding starts with a sub-set of the LP constraints, and iteratively adds violated constraints until an optimum of the original LP is found. Usually only a tiny fraction of the original constraints need to be reinstated, leading to huge efficiency gains compared to ordinary LP decoding.

Here we describe a modification of the adaptive LP decoder that results in a maximum likelihood (ML) decoder. Whenever the adaptive LP decoder returns a pseudo-codeword rather than a codeword, we add an integer constraint on the least certain symbol of the pseudo-codeword. For certain codes, and especially in the high-SNR (error floor) regime, only a few integer constraints are required to force the resultant mixed -integer LP to the ML solution. We demonstrate that our approach can efficiently achieve the optimal ML decoding performance on a (155.64) LDPC code introduced by Tanner et al.