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An Upper Bound to the Undetected Error Exponent with Erasure Decoding at Positive Rates

Year: 2026

Type: preprint

Abstract: We study the undetected-error exponent of discrete memoryless channels with erasure decoding. Assuming that the undetected-error and erasure probabilities vanish, we derive an upper bound on the undetected-error exponent at positive rates. The bound uses Somekh-Baruch's genie-aided argument where an auxiliary output provides the decoder with a list of codewords. It recovers Telatar's tight rate-zero converse and is at least as tight as the straight-line bound. A numerical example shows that the improvement over the straight-line bound can be strict.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15420

Authors: Moeini, Seyed AmirPouya, Dalai, Marco, Fàbregas, Albert Guillén i

Institutions: University of Cambridge, University of Brescia

Language: English

Topic: Error Correcting Code Techniques

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221815980

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