Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintCC BY-NC-SA 4.0arXiv

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

  • Seyed AmirPouya Moeini
  • Marco Dalai
  • Albert Guillén i Fàbregas
Open at sourcePDFDOICite

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.

Related

  1. Decoding Error Probability of the Random Code Ensemble over the Erasure Channel
    Chin Hei Chan
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  2. Spatially Coupled MacKay-Neal/Hsu-Anastasopoulos CSS Codes Achieve the Quantum-Erasure Hashing Bound by Seeded BP Decoding
    Kenta Kasai
    arXivPreprintarXiv licenceFull textGeneral mathematicsQuantum physics & quantum informationarXiv
  3. A new upper bound for the irrationality exponent of zeta(3)
    David Niedbala Giraudin
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. A new upper bound for the irrationality exponent of ζ(2)
    David Niedbala Giraudin
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Ideal-Smooth Sets and an Explicit Upper Bound for the Real Sum-Product Exponent
    Kaiqiang Zhang, Yuanguo Zeng, Yuyu Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{moeini2026upper,
  title = {{An Upper Bound to the Undetected Error Exponent with Erasure Decoding at Positive Rates}},
  author = {Seyed AmirPouya Moeini and Marco Dalai and Albert Guillén i Fàbregas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15420},
  eprint = {2610.15420},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15420},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - An Upper Bound to the Undetected Error Exponent with Erasure Decoding at Positive Rates
AU  - Seyed AmirPouya Moeini
AU  - Marco Dalai
AU  - Albert Guillén i Fàbregas
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15420
UR  - https://arxiv.org/abs/2610.15420
AB  - 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.
ER  -