ML decoding via mixed-integer adaptive linear programming

S. Draper, J. Yedidia, Yige Wang
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引用次数: 43

Abstract

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.
ML解码通过混合整数自适应线性规划
线性规划(LP)解码是由Feldman等人提出的。通知。Theory(2005年3月)作为一种解码二进制低密度奇偶校验码的新方法。Taghavi和Siegel (Proc. ISIT 2006)描述了一种计算简化的解码方法,他们称之为“自适应”LP解码。自适应LP解码从LP约束的子集开始,迭代地增加违反的约束,直到找到原始LP的最优解。通常只需要恢复原始约束的一小部分,与普通LP解码相比,可以获得巨大的效率提升。在这里,我们描述了自适应LP解码器的修改,从而产生最大似然(ML)解码器。每当自适应LP解码器返回伪码字而不是码字时,我们在伪码字的最小确定符号上添加整数约束。对于某些代码,特别是在高信噪比(错误层)条件下,只需要几个整数约束就可以将混合整数LP强制到ML解决方案中。我们证明了我们的方法可以有效地在Tanner等人引入的(155,64)LDPC代码上实现最佳的ML解码性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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