发表机构
Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对对称马尔可夫噪声下的固定度空间耦合MacKay-Neal码，证明容量准则，通过条件熵修正和两状态后验收缩，实现BMS信道归约，达到阈值饱和。
AI 中文摘要
我们证明了在加性对称马尔可夫噪声上，固定度空间耦合MacKay--Neal码的一个容量准则。噪声以概率$p$翻转比特，因此该信道有一个参数，容量为$1-h_2(p)$。对于每个整数$\ell\geq4$且满足$3/\ell<1-h_2(p)$，匹配的有限窗口BCJR和和积译码允许码序列（可能依赖于$p$），其实际码率趋于$3/\ell$，且平均信息比特错误趋于零。证明过程与GEC到BEC的论证平行：一个条件熵修正将BMS不动点正性转移到有记忆的信道。该修正还涵盖了有效BMS信道的容量赤字。一个两状态后验收缩提供了阈值饱和所需的额外导数界。该结果使用了所引用的BMS正性定理，其中对于$\ell\geq33$有解析证明，对于$4\leq\ell\leq32$有精确区间证书。
英文摘要
We prove a capacity criterion for fixed-degree spatially coupled MacKay--Neal codes on additive symmetric Markov noise. The noise bit flips with probability $p$, so the channel has one parameter and capacity $1-h_2(p)$. For every integer $\ell\geq4$ with $3/\ell<1-h_2(p)$, matched finite-window BCJR and sum-product decoding admit code sequences, possibly depending on $p$, with actual rate tending to $3/\ell$ and vanishing average information-bit error. The proof parallels the GEC-to-BEC argument: a conditional-entropy correction transfers BMS fixed-point positivity to the channel with memory. The correction also covers a capacity deficit of the effective BMS channel. A two-state posterior contraction supplies the additional derivative bound needed for threshold saturation. The result uses the cited BMS positivity theorem, with an analytic proof for $\ell\geq33$ and exact interval certificates for $4\leq\ell\leq32$.
Comments15 pages
