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首页> 外文期刊>Information Theory, IEEE Transactions on >The Cycle Consistency Matrix Approach to Absorbing Sets in Separable Circulant-Based LDPC Codes
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The Cycle Consistency Matrix Approach to Absorbing Sets in Separable Circulant-Based LDPC Codes

机译：可循环循环LDPC码中吸收集的循环一致性矩阵法

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摘要

For low-density parity-check (LDPC) codes operating over additive white Gaussian noise channels and decoded using message-passing decoders with limited precision, absorbing sets have been shown to be a key factor in error floor behavior. Focusing on this scenario, this paper introduces the cycle consistency matrix (CCM) as a powerful analytical tool for characterizing and avoiding absorbing sets in separable circulant-based (SCB) LDPC codes. SCB codes include a wide variety of regular LDPC codes such as array-based LDPC codes as well as many common quasi-cyclic codes. As a consequence of its cycle structure, each potential absorbing set in an SCB LDPC code has a CCM, and an absorbing set can be present in an SCB LDPC code only if the associated CCM has a nontrivial null space. CCM-based analysis can determine the multiplicity of an absorbing set in an SCB code, and CCM-based constructions avoid certain small absorbing sets completely. While these techniques can be applied to an SCB code of any rate, lower rate SCB codes can usually avoid small absorbing sets because of their higher variable-node degree. This paper focuses attention on the high-rate scenario in which the CCM constructions provide the most benefit. Simulation results demonstrate that under limited-precision decoding the new codes have steeper error-floor slopes and can provide one order of magnitude of improvement in the low-frame-error-rate region.
机译：对于在加性白高斯噪声通道上运行并使用消息传递解码器以有限精度进行解码的低密度奇偶校验（LDPC）码，吸收集已被证明是错误本底行为的关键因素。针对这种情况，本文介绍了循环一致性矩阵（CCM）作为一种强大的分析工具，用于表征和避免基于可循环循环（SCB）的LDPC码中的吸收集。 SCB码包括各种常规LDPC码，例如基于阵列的LDPC码以及许多常见的准循环码。由于其循环结构，SCB LDPC码中的每个电势吸收集都具有一个CCM，并且只有在关联的CCM具有非平凡的空白空间时，吸收集才能出现在SCB LDPC码中。基于CCM的分析可以确定SCB代码中吸收集的多样性，而基于CCM的构造完全避免了某些小的吸收集。尽管这些技术可以应用于任何速率的SCB代码，但是较低速率的SCB代码通常可以避免较小的吸收集，因为它们的可变节点度较高。本文关注于CCM结构提供最大收益的高速率方案。仿真结果表明，在有限精度解码下，新代码的误码率斜率更加陡峭，并且可以在低误码率区域提供一个数量级的改进。

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