Two classes of QC-LDPC cycle codes approaching Gallager lower bound
Two classes of QC-LDPC cycle codes approaching Gallager lower bound
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DOI：
10.1007/s11432-018-9778-x
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Hengzhou Xu;Huaan Li;Mengmeng Xu;Dan Feng;Hai Zhu
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文献类型：
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作者：
Hengzhou Xu;Huaan Li;Mengmeng Xu;Dan Feng;Hai Zhu
亲爱的编辑，许多研究结果表明，在等比特长度的情况下，短的非二进制LDPC码的性能比二进制LDPC码高约1dB[1-3]。此外，多进制LDPC码具有误码率低、迭代译码收敛快、纠正突发错误能力强等优点。但其应用的障碍是较高的译码复杂度。近年来，人们对多进制LDPC码的低复杂度译码算法进行了大量的研究[4]。值得注意的是，这些低复杂度算法都是在迭代译码的框架下进行的。因此，设计适合迭代算法的最小距离较大的多进制LDPC码是很有意义的。对于给定的分组长度，多进制LDPC码的性能随着其有限域大小的增加而越来越好。当有限域足够大时，增加的编码增益可以忽略不计，然后最佳非二进制LDPC码的奇偶校验矩阵中的列重趋于2。为了便于硬件实现，应考虑准循环(QC)结构。本文研究了一类列重为2、行重为ρ的二进制QC-LDPC码。注意，这类码被称为(2，ρ)-正则QC-LDPC循环码。通过用非二进制有限域的非零元素替换QC-LDPC循环码的奇偶校验矩阵中的1‘S，
Dear editor, Many research results show that, for equivalent bit length, short nonbinary LDPC codes outperform binary LDPC codes by about 1 dB [1–3]. Moreover, nonbinary LDPC codes have lower errorfloor, fast iterative decoding convergence, and strong ability of correcting burst errors. But the roadblock to their application is the high decoding complexity. Recently, significant studies on the low-complexity decoding algorithms of nonbinary LDPC codes have been done [4]. It is noticeable that these low-complexity algorithms are under the frame of iterative decoding. Hence, it is interesting to design nonbinary LDPC codes with large minimum distance and suitable for the iterative algorithms.For a given block length, nonbinary LDPC codes perform better and better with the increase of their finite field size. When the finite field size is sufficiently large, the increased coding gain becomes negligible, and then the column weight in the parity-check matrices of the best nonbinary LDPC codes tends to 2. In order to facilitate the hardware implementation, quasi-cyclic (QC) structure should be considered. In this study, we study a class of binary QC-LDPC codes with column weight 2 and row weight ρ. Notice that this class of codes is referred to as (2, ρ)-regular QC-LDPC cycle codes. By replacing 1’s in the parity-check matrices of QC-LDPC cycle codes with nonzero elements of nonbinary finite fields,