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 Probl. Peredachi Inf., 2005, Volume 41, Issue 3, Pages 3–16 (Mi ppi102)

Information Theory

Sufficient Conditions for Monotonicity of the Undetected Error Probability for Large Channel Error Probabilities

R. D. Dodunekovaa, E. Nikolovab

a Department of Mathematical Sciences, Chalmers University of Technology and the University of Göteborg
b Burgas Free University

Abstract: The performance of a linear error-detecting code in a symmetric memoryless channel is characterized by its probability of undetected error, which is a function of the channel symbol error probability, involving basic parameters of a code and its weight distribution. However, the code weight distribution is known for relatively few codes since its computation is an NP-hard problem. It should therefore be useful to have criteria for properness and goodness in error detection that do not involve the code weight distribution. In this work we give two such criteria. We show that a binary linear code $C$ of length $n$ and its dual code $C^\perp$ of minimum code distance $d^\perp$ are proper for error detection whenever $d^\perp\geqslant\lfloor n/2\rfloor+1$, and that $C$ is proper in the interval $[(n+1-2d^\perp)/(n-d^\perp),1/2]$ whenever $\lceil n/3\rceil+1\leqslant d^\perp\leqslant\lfloor n/2\rfloor$. We also provide examples, mostly of Griesmer codes and their duals, that satisfy the above conditions.

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English version:
Problems of Information Transmission, 2005, 41:3, 187–198

Bibliographic databases:

UDC: 621.391.1:519.2
Revised: 21.02.2005

Citation: R. D. Dodunekova, E. Nikolova, “Sufficient Conditions for Monotonicity of the Undetected Error Probability for Large Channel Error Probabilities”, Probl. Peredachi Inf., 41:3 (2005), 3–16; Problems Inform. Transmission, 41:3 (2005), 187–198

Citation in format AMSBIB
\Bibitem{DodNik05} \by R.~D.~Dodunekova, E.~Nikolova \paper Sufficient Conditions for Monotonicity of the Undetected Error Probability for Large Channel Error Probabilities \jour Probl. Peredachi Inf. \yr 2005 \vol 41 \issue 3 \pages 3--16 \mathnet{http://mi.mathnet.ru/ppi102} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2163846} \zmath{https://zbmath.org/?q=an:1104.94010} \transl \jour Problems Inform. Transmission \yr 2005 \vol 41 \issue 3 \pages 187--198 \crossref{https://doi.org/10.1007/s11122-005-0023-5} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Franekova M., Rastocny K., “Problems of Safety Codes Evaluation in Practical Applications”, Transport System Telematics, Communications in Computer and Information Science, 104, 2010, 232–242
2. Davydov A.A. Marcugini S. Pambianco F., “New Results on Binary Codes Obtained By Doubling Construction”, Cybern. Inf. Technol., 18:5, SI (2018), 63–76
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