Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Scarlett, Jonathan
Institution: National University of Singapore
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214230428