Effects of Single-Cycle Structure on Iterative Decoding of Low-Density Parity-Check Codes
Effects of Single-Cycle Structure on Iterative Decoding of Low-Density Parity-Check Codes
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DOI：
10.1109/tit.2012.2216252
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发表时间：
2010-10
影响因子：
2.5
通讯作者：
R. Mori;Toshiyuki TANAKA;K. Kasai;K. Sakaniwa
中科院分区：
文献类型：
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作者：
R. Mori;Toshiyuki TANAKA;K. Kasai;K. Sakaniwa
我们考虑了使用低密度奇偶校验(LDPC)码和置信度传播(BP)译码的二进制擦除信道(BEC)上的通信。对于固定的BP迭代次数，当块长度趋于无穷大时，误码率逼近一个极限值，该极限值是通过密度进化获得的。当块长度n趋于无穷大时，有限块长度校正的行为类似于α(ε，t)/n+Θ(n-2)，其中α(ε，t)表示由所考虑的码集、迭代次数t和BEC的擦除概率ε确定的特定常数。在本文中，我们推导了一组递推公式，它允许计算标准不规则系综常数α(ε，t)。图的显性差α(ε，t)/n可以看作是局部图的无圈结构和单圈结构的影响。此外，通过数值模拟证实，即使对于较小的块长度，使用α(ε，t)来估计误码率也是准确的。
We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as the blocklength tends to infinity, and the limit is obtained via density evolution. The finite-blocklength correction behaves like α(ε,t)/n+Θ(n-2) as the blocklength n tends to infinity where α(ε,t) denotes a specific constant determined by the code ensemble considered, the number t of iterations, and the erasure probability ε of the BEC. In this paper, we derive a set of recursive formulas which allows the evaluation of the constant α(ε,t) for standard irregular ensembles. The dominant difference α(ε,t)/n can be considered as effects of cycle-free and single-cycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using α(ε,t) is accurate even for small blocklengths.