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首页> 外文期刊>IEEE Transactions on Information Theory >The ADMM Penalized Decoder for LDPC Codes
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The ADMM Penalized Decoder for LDPC Codes

机译：LDPC码的ADMM惩罚式解码器

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Linear programming (LP) decoding for low-density parity-check codes was introduced by Feldman and has been shown to have theoretical guarantees in several regimes. Furthermore, it has been reported in the literature—via simulation and via instanton analysis—that LP decoding displays better error rate performance at high signal-to-noise ratios (SNR) than does belief propagation (BP) decoding. However, at low SNRs, LP decoding is observed to have worse performance than BP. In this paper, we seek to improve LP decoding at low SNRs while maintaining LP decoding’s high SNR performance. Our main contribution is a new class of decoders obtained by applying the alternating direction method of multipliers (ADMM) algorithm to a set of non-convex optimization problems. These non-convex problems are constructed by adding a penalty term to the objective of LP decoding. The goal of the penalty is to make pseudocodewords, which are non-integer vertices of the LP relaxation, more costly. We name this class of decoders—ADMM penalized decoders. For low and moderate SNRs, we simulate ADMM penalized decoding with and penalties. We find that these decoders can outperform both BP and LP decoding. For high SNRs, where it is difficult to obtain data via simulation, we use an instanton analysis and find that, asymptotically, ADMM penalized decoding performs better than BP but not as well as LP. Unfortunately, since ADMM penalized decoding is not a convex program, we have not been successful in developing theoretical guarantees. However, the non-convex program can be approximated using a sequence of linear programs; an approach that yields a reweighted LP decoder. We show that a two-round reweighted LP decoder has an improved theoretical recovery threshold when compared wi- h LP decoding. In addition, we find via simulation that reweighted LP decoding significantly attains lower error rates than LP decoding at low SNRs.
机译：费尔德曼（Feldman）引入了用于低密度奇偶校验码的线性编程（LP）解码，并已证明在几种情况下具有理论保证。此外，在文献中（通过仿真和通过瞬时分析）已经报道，与置信传播（BP）解码相比，LP解码在高信噪比（SNR）时显示出更好的误码率性能。但是，在低SNR时，观察到LP解码的性能比BP差。在本文中，我们力求在保持LP解码的高SNR性能的同时改善低SNR的LP解码。我们的主要贡献是通过将乘数交替方向方法（ADMM）算法应用于一组非凸优化问题而获得的新型解码器。这些非凸问题是通过将惩罚项添加到LP解码的目的而构造的。惩罚的目的是使伪代码字（其为LP松弛的非整数顶点）的成本更高。我们将这类解码器命名为ADMM惩罚式解码器。对于低和中等SNR，我们使用和惩罚来模拟ADMM惩罚解码。我们发现这些解码器可以胜过BP和LP解码。对于难以通过仿真获得数据的高SNR，我们使用实例分析，发现渐近地，ADMM惩罚式解码的性能优于BP，但不如LP。不幸的是，由于ADMM惩罚式解码不是凸程序，因此我们在开发理论保证方面没有成功。但是，可以使用一系列线性程序来近似非凸程序。产生重新加权的LP解码器的方法。我们证明，与LP解码相比，两轮重加权LP解码器具有更高的理论恢复阈值。此外，我们通过仿真发现，与低信噪比下的LP解码相比，重新加权LP解码显着降低了误码率。

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