Large deviations behavior of the logarithmic error probability of random codes

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• dc.contributor.author Tamir, Ran
• dc.contributor.author Merhav, Neri
• dc.contributor.author Weinberger, Nir
• dc.contributor.author Guillén i Fábregas, A. (Albert)
• dc.date.accessioned 2021-04-21T08:35:54Z
• dc.date.issued 2020
• dc.description.abstract This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double-exponentially small; upper and lower bounds to the double-exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables.
• dc.description.sponsorship The research of R. Tamir and N. Merhav was supported by Israel Science Foundation (ISF) grant no. 137/18. The research of N. Weinberger was partially supported by the MIT–Technion fellowship, and the Viterbi scholarship, Technion. The research of A. Guillen i F ´ abregas was funded in part by the European Research Council under ERC grant 725411 and by the Spanish Ministry of Economy and Competitiveness under grant TEC2016-78434-C3-1-R. This paper was presented in part at the 2019 IEEE International Symposium on Information Theory, Paris, France, 7-12 July, 2019.
• dc.format.mimetype application/pdf
• dc.identifier.citation Tamir R, Merhav N, Weinberger N, Guillén i Fàbregas A. Large deviations behavior of the logarithmic error probability of random codes. IEEE Trans Inf Theory. 2020;66(11):6635-59. DOI: 10.1109/TIT.2020.2995136
• dc.identifier.doi http://dx.doi.org/10.1109/TIT.2020.2995136
• dc.identifier.issn 0018-9448
• dc.identifier.uri http://hdl.handle.net/10230/47176
• dc.language.iso eng
• dc.publisher Institute of Electrical and Electronics Engineers (IEEE)
• dc.relation.ispartof IEEE Transactions on Information Theory. 2020;66(11):6635-59
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/725411
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/TEC2016-78434-C3-1-R
• dc.rights © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. http://dx.doi.org/10.1109/TIT.2020.2995136
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Error exponent
• dc.subject.keyword Expurgated exponent
• dc.subject.keyword Large deviations
• dc.subject.keyword Typical random code
• dc.title Large deviations behavior of the logarithmic error probability of random codes
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion