On Universal LDPC Code Ensembles Over Memoryless Symmetric Channels
On Universal LDPC Code Ensembles Over Memoryless Symmetric Channels
复制标题
无记忆对称信道上的通用 LDPC 码集成
DOI：
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发表时间：
2011
影响因子：
2.5
通讯作者：
Boaz Shuval
中科院分区：
文献类型：
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作者：
I. Sason;Boaz Shuval
在各种渠道上实现可靠的沟通的鲁棒校正代码的设计具有极大的理论和实际兴趣。此类代码被称为通用。本文考虑了低密度平价检查（LDPC）代码在无内存二元输入输出对称（MBIOS）渠道的家庭中的普遍性。普遍性被认为是信仰传播（BP）和最大样本（ML）解码的普遍性。对于BP解码案例，我们得出了一种基于密度进化的分析方法，用于设计与MBIOS通道各个家族的普遍存在的LDPC代码集合。我们还得出了BP解码下的LDPC代码合奏通用性的必要条件；该条件用于为能力的普遍可实现的范围提供界限。这些结果使我们能够根据基于通道的Bhattacharyya参数提供可靠/不可靠的通信条件。对于ML解码案例，我们证明正确选择的常规LDPC代码合奏是针对Equi-Eapacity MBIOS频道的普遍实现能力实现的，并将此结果扩展到刺穿常规的LDPC代码集合。
A design of robust error-correcting codes that achieve reliable communication over various channels is of great theoretical and practical interest. Such codes are termed universal. This paper considers the universality of low-density parity-check (LDPC) code ensembles over families of memoryless binary-input output-symmetric (MBIOS) channels. Universality is considered both under belief-propagation (BP) and maximum-likelihood (ML) decoding. For the BP decoding case, we derive a density-evolution-based analytical method for designing LDPC code ensembles that are universal over various families of MBIOS channels. We also derive a necessary condition for universality of LDPC code ensembles under BP decoding; this condition is used to provide bounds on the universally achievable fraction of capacity. These results enable us to provide conditions for reliable/unreliable communications under BP decoding that are based on the Bhattacharyya parameter of the channel. For the ML decoding case, we prove that properly selected regular LDPC code ensembles are universally capacity-achieving for the set of equi-capacity MBIOS channels and extend this result to punctured regular LDPC code ensembles.