Fast Linear-Programming decoding of LDPC codes over GF(2m)
Fast Linear-Programming decoding of LDPC codes over GF(2m)
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发表时间：
2012-10
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通讯作者：
J. Honda;Hirosuke Yamamoto
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作者：
J. Honda;Hirosuke Yamamoto
近年来，线性规划（LP）译码作为LDPC码置信传播（BP）译码的一种替代方案受到广泛关注。对于BP译码来说，非二进制LDPC码可以显著提高译码错误概率。另一方面，Flanagan等人提出了有限环上LDPC码的LP解码方案。虽然他们的方案适用于有限域上的LDPC码，但LP中的变量数量迅速增长，因此，随着域大小的增加，其实现变得更加困难。为了克服这个缺陷，我们提出了一个新的LP解码方案的GF（2m），其中变量的数量线性增加字段大小。虽然我们的计划放宽了最大似然解码问题更宽松的LP问题比他们的计划，恶化的解码错误概率是小的。
Recently Linear Programming (LP) decoding is attracting much attention as an alternative to Belief Propagation (BP) decoding for LDPC codes. It is well known for the BP decoding that nonbinary LDPC codes can improve the decoding error probability considerably. On the other hand, Flanagan et al. proposed an LP decoding scheme for LDPC codes over finite rings. Although their scheme is applicable to LDPC codes over finite fields, the number of variables in the LP grows rapidly and hence, its implementation becomes harder as the field size increases. To overcome this defect we propose a new LP decoding scheme for GF(2m), in which the number of variables increases linearly in the field size. Although our scheme relaxes a maximum likelihood decoding problem more loosely to an LP problem than their scheme, the deterioration of the decoding error probability is small.