We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard block codes. We develop an efficient decoding algorithm that combines pipeline decoding and layered scheduling for the decoding of SC-PLDPCH-CCs, and analyze the latency and complexity of the decoder. To estimate the decoding thresholds of SC-PLDPCH-CCs, we first propose a layered protograph extrinsic information transfer (PEXIT) algorithm to evaluate the thresholds of spatially coupled PLDPC-Hadamard terminated codes (SC-PLDPCH-TDCs) with a moderate coupling length. With the use of the proposed layered PEXIT method, we develop a genetic algorithm to find good SC-PLDPCH-TDCs in a systematic way. Then we extend the coupling length of these SC-PLDPCH-TDCs to form good SC-PLDPCH-CCs. Results show that our constructed SC-PLDPCH-CCs can achieve comparable thresholds to the block code counterparts. Simulations illustrate the superiority of the SC-PLDPCH-CCs over the block code counterparts and other state-of-the-art low-rate codes in terms of error performance. For the rate-0.00295 SC-PLDPCH-CC, a bit error rate of 10−5 is achieved at Eb/N0=−1.465E_{b}/N_{0} = -1.465 dB, which is only 0.125 dB from the ultimate Shannon limit.

中文翻译：

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空间耦合 PLDPC-Hadamard 卷积码


我们提出了一种新型的终极逼近香农极限码，称为空间耦合原形图低密度奇偶校验哈达玛卷积码（SC-PLDPCH-CC），它是通过空间耦合 PLDPC-哈达玛块码构造的。我们开发了一种结合流水线解码和分层调度的高效解码算法，用于 SC-PLDPCH-CC 的解码，并分析了解码器的延迟和复杂性。为了估计 SC-PLDPCH-CC 的解码阈值，我们首先提出了一种分层原图外在信息传输（PEXIT）算法来评估具有中等耦合长度的空间耦合 PLDPC-Hadamard 终止码（SC-PLDPCH-TDC）的阈值。通过使用所提出的分层 PEXIT 方法，我们开发了一种遗传算法，以系统的方式找到良好的 SC-PLDPCH-TDC。然后我们延长这些 SC-PLDPCH-TDC 的耦合长度以形成良好的 SC-PLDPCH-CC。结果表明，我们构建的 SC-PLDPCH-CC 可以达到与块码对应物相当的阈值。仿真说明了 SC-PLDPCH-CC 在误码性能方面优于块码对应物和其他最先进的低速率码。对于速率为 0.00295 SC-PLDPCH-CC，在 Eb/N0=−1.465E_{b}/N_{0} = -1.465 dB 时实现了 10−5 的误码率，与最终值仅相差 0.125 dB。香农极限。