Communication over the binary erasure channel (BEC) using low-densityparity-check (LDPC) codes and belief propagation (BP) decoding is considered.The average bit error probability of an irregular LDPC code ensemble after afixed number of iterations converges to a limit, which is calculated viadensity evolution, as the blocklength $n$ tends to infinity. The differencebetween the bit error probability with blocklength $n$ and thelarge-blocklength limit behaves asymptotically like $\alpha/n$, where thecoefficient $\alpha$ depends on the ensemble, the number of iterations and theerasure probability of the BEC\null. In [1], $\alpha$ is calculated for regularensembles. In this paper, $\alpha$ for irregular expurgated ensembles isderived. It is demonstrated that convergence of numerical estimates of $\alpha$to the analytic result is significantly fast for irregular unexpurgatedensembles.
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机译：考虑了使用低密度奇偶校验（LDPC）码和置信度传播（BP）解码的二进制擦除信道（BEC）上的通信。固定迭代次数后，不规则LDPC码集合的平均误码率收敛到一个极限，这是通过密度变化计算的，因为块长$ n $趋于无穷大。块长度为$ n $的误码概率与大块长度限制之间的差表现为渐进式，类似于$ \ alpha / n $，其中系数$ \ alpha $取决于整体，迭代次数和BEC \ null的擦除概率。在[1]中，$ \ alpha $是为规则集合计算的。在本文中，推导了不规则磨合乐团的\ alpha。结果表明，对于不规则的未经吹奏的集合，\ alpha $的数值估计值与分析结果的收敛速度非常快。
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