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首页> 外文期刊>Information Theory, IEEE Transactions on >Capacity-Achieving Codes With Bounded Graphical Complexity and Maximum Likelihood Decoding
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Capacity-Achieving Codes With Bounded Graphical Complexity and Maximum Likelihood Decoding

机译：具有有限图形复杂性和最大似然解码的容量实现代码

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摘要

In this paper, the existence of capacity-achieving codes for memoryless binary-input output-symmetric (MBIOS) channels under maximum-likelihood (ML) decoding with bounded graphical complexity is investigated. Graphical complexity of a code is defined as the number of edges in the graphical representation of the code per information bit and is proportional to the decoding complexity per information bit per iteration under iterative decoding. Irregular repeat-accumulate (IRA) codes are studied first. Utilizing the asymptotic average weight distribution (AAWD) of these codes and invoking Divsalar's bound on the binary-input additive white Gaussian noise (BIAWGN) channel, it is shown that simple nonsystematic IRA ensembles outperform systematic IRA and regular low-density parity-check (LDPC) ensembles with the same graphical complexity, and are at most 0.124 dB away from the Shannon limit. However, a conclusive result as to whether these nonsystematic IRA codes can really achieve capacity cannot be reached. Motivated by this inconclusive result, a new family of codes is proposed, called low-density parity-check and generator matrix (LDPC-GM) codes, which are serially concatenated codes with an outer LDPC code and an inner low-density generator matrix (LDGM) code. It is shown that these codes can achieve capacity on any MBIOS channel using ML decoding and also achieve capacity on any BEC using belief propagation (BP) decoding, both with bounded graphical complexity. Moreover, it is shown that, under certain conditions, these capacity-achieving codes have linearly increasing minimum distances and achieve the asymptotic Gilbert-Varshamov bound for all rates.
机译：在本文中，研究了具有有限图形复杂度的最大似然（ML）解码下无记忆二进制输入输出对称（MBIOS）通道的容量实现代码的存在。代码的图形复杂度定义为每个信息位的代码图形表示中的边数，并且与迭代解码下每次迭代的每个信息位的解码复杂度成比例。首先研究不规则重复累积（IRA）码。利用这些代码的渐近平均权重分布（AAWD）并调用二进制输入的加性高斯白噪声（BIAWGN）通道上的Divsalar界限，表明简单的非系统性IRA的性能优于系统性IRA和常规的低密度奇偶校验（ LDPC）具有相同的图形复杂度，并且与Shannon限制相距最多0.124 dB。但是，无法得出关于这些非系统性IRA代码是否真正可以实现容量的结论性结果。受此不确定性结果的启发，提出了一种新的代码系列，称为低密度奇偶校验和生成器矩阵（LDPC-GM）代码，它们是由外部LDPC码和内部低密度生成器矩阵（ LDGM）代码。结果表明，这些代码可以使用ML解码在任何MBIOS通道上实现容量，并且还可以使用置信传播（BP）解码在任何BEC上实现容量，两者均具有有限的图形复杂性。此外，表明在某些条件下，这些实现容量的代码具有线性增加的最小距离，并在所有速率下达到渐近吉尔伯特-瓦尔沙莫夫边界。

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