On Universal Properties of Capacity-Approaching LDPC Code Ensembles
On Universal Properties of Capacity-Approaching LDPC Code Ensembles
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DOI：
10.1109/tit.2009.2021305
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发表时间：
2007-09
影响因子：
2.5
通讯作者：
I. Sason
中科院分区：
文献类型：
--
作者：
I. Sason
本文的重点是衍生能力的低密度奇偶校验检查（LDPC）代码集合的某些通用性能，其传输发生在无内存的二进制输入输出对称（MBIOS）通道上。通过信息理论界限来考虑度分布，图形复杂性和两部分图中基本周期的数量的性质。这些边界是根据目标块/位误差概率和差距（以速率）到容量的差异表示的。对于任何解码算法而言，大多数界限都是一般的，而另一些界限则证明是在信仰传播（BP）解码之下。在某个解码算法下证明这些界限，也可以在任何次优解码算法下自动验证它们。对这些界限的正确修改使得它们对于表现出给定容量的所有MBIO频道集合。程度分布和图形复杂性的边界适用于有限长度的LDPC代码以及无限块长度的渐近情况。将界限与BP解码下的容量吸引力的LDPC代码合奏进行了比较，并且显示出很大的信息，并且易于计算。最后，考虑了一些有趣的开放问题。
This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity, and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any suboptimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.