AI 中文总结
研究通过乘积编码将比特级可靠性转换为块级可靠性，编码结合特定行码与列码，解码分两步，证明在一定条件下乘积码块误码概率趋近于零，还构建了能实现任意固定BMS信道容量的乘积码族。
AI 中文摘要
本文表明乘积编码可在相同渐近速率下将比特级可靠性转换为块级可靠性。编码过程结合了目标速率且误码概率趋近于零的行码以及具有有界距离纠错能力的高速率列码。解码时先解行码，再解列码。若列校正半径超过残留误码概率且列长度足够大，乘积码的块误码概率趋近于零。这样可将比特级容量实现族转换为块级容量实现乘积码族。作为应用，构建了实现任意固定BMS信道容量的RM - BCH乘积码族。
英文摘要
This paper shows that bit-level reliability can be converted into block-level reliability for binary codes over BMS channels through Forney's concatenation scheme. The construction concatenates an inner code of rate R-o(1) and vanishing bit-error probability εwith an outer code of rate 1-o(1) equipped with a bounded-distance decoder. We show that, when the outer correction radius exceeds εand a suitable large-deviation condition holds, the concatenated code has rate R-o(1) and vanishing block-error probability. Hence, a family with vanishing bit-error probability for rates below capacity can be converted into a capacity-achieving concatenated-code family. We further show that, when binary BCH codes are used as outer codes, inner codes with bit-error probability ε=o(1/\log\log n) can be converted into a capacity-achieving concatenated family.
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