We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.

中文翻译：

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BEC上窗口解码下空间耦合LDPC码的有限长度缩放

我们分析了二进制擦除信道上窗口解码下空间耦合低密度奇偶校验 (SC-LDPC) 码的有限长度性能。特别是，我们提出了 Olmos 和 Urbanke 对完全置信传播 (BP) 解码下终止 SC-LDPC 集成的帧错误率 (FER) 的缩放定律的改进。改进的缩放定律将解码过程建模为两个独立的 Ornstein-Uhlenbeck 过程，对应于向耦合链中心传播的两个解码波，用于终止 SC-LDPC 码。然后，我们扩展了所提出的缩放定律，以在更实用的滑动窗口解码下预测（终止的）SC-LDPC 码集合的性能。最后，我们扩展了这个框架来预测 SC-LDPC 码集合的误码率 (BER) 和误块率 (BLER)。