诊断二进制输入信道的被驳斥的失配解码逆定理
Diagnosing the Refuted Mismatched Decoding Converse for Binary-Input Channels
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文诊断了Balakirsky关于二进制输入信道失配解码逆定理的证明，指出其置换引理及两个具体步骤存在缺陷，并证明相关命题在一般情况下不成立。
AI中文摘要：
我们重新审视了针对二进制输入离散无记忆信道的失配解码的声称逆定理（Balakirsky, 1995），以及后续通过数值反例驳斥该逆定理的工作（Scarlett, Somekh-Baruch, Martinez, 和 Guillén i Fàbregas, 2015）。现有理解中的一个显著空白是，在Balakirsky的分析中未识别出具体缺陷。在本文中，我们对Balakirsky的证明进行了“诊断”，并证明：（i）他的置换引理是有缺陷的，无论其组合近似引理是否正确；（ii）关于受限码和选择器序列，至少存在两个具体的错误步骤，这些步骤似乎不太可能通过局部修复来纠正；（iii）使用这些错误步骤的命题在一般情况下是错误的。
英文摘要：
We revisit the claimed converse theorem for mismatched decoding over binary-input discrete memoryless channels (Balakirsky, 1995) and the subsequent work refuting this converse via a numerical counter-example (Scarlett, Somekh-Baruch, Martinez, and Guillén i Fàbregas, 2015). A notable gap in the existing understanding is that no concrete flaw was identified in Balakirsky's analysis. In this paper, Balakirsky's proof is "diagnosed", and it is demonstrated that (i) his permutation lemma is flawed regardless of the correctness of his combinatorial approximation lemma; (ii) there are at least two specific incorrect steps regarding restricted codes and selector sequences, and these appear to be unlikely to admit a local repair; and (iii) the proposition in which these incorrect steps are used is false in general.
