The Error Exponent of Generalized Random-Gilbert Varshamov Codes

Anelia Somekh-Baruch; Jonathan Scarlett; Albert Guilleni Fabregas

doi:10.1109/isit.2018.8437312

The Error Exponent of Generalized Random-Gilbert Varshamov Codes

Anelia Somekh-Baruch, Jonathan Scarlett, Albert Guilleni Fabregas

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We introduce a random code construction for channel coding in which the codewords are constrained to be well-separated according to a given distance function, analogously to an existing construction attaining the Gilbert-Varshamov bound. We derive an achievable error exponent for this construction, and prove its tightness with respect to the ensemble average. We show that the exponent recovers the Csiszár and Körner exponent as a special case by choosing the distance function to be the negative of the empirical mutual information. We further establish the optimality of this distance function with respect to the exponent of the random coding scheme.

Original language	English
Title of host publication	2018 IEEE International Symposium on Information Theory, ISIT 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2361-2365
Number of pages	5
ISBN (Print)	9781538647806
DOIs	https://doi.org/10.1109/isit.2018.8437312
State	Published - 15 Aug 2018
Event	2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: 17 Jun 2018 → 22 Jun 2018

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2018-June
ISSN (Print)	2157-8095

Conference

Conference	2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/Territory	United States
City	Vail
Period	17/06/18 → 22/06/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

Funding

This work was supported in part by the Israel Science Foundation under grant 631/17, the European Research Council under Grant 725411, the Spanish Ministry of Economy and Competitiveness under Grant TEC2016-78434-C3-1-R, and an NUS Startup Grant.

Funders	Funder number
Spanish Ministry of Economy and Competitiveness	TEC2016-78434-C3-1-R
Horizon 2020 Framework Programme	725411
European Commission
National University of Singapore
Israel Science Foundation	631/17

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10.1109/isit.2018.8437312

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Somekh-Baruch, A., Scarlett, J., & Guilleni Fabregas, A. (2018). The Error Exponent of Generalized Random-Gilbert Varshamov Codes. In 2018 IEEE International Symposium on Information Theory, ISIT 2018 (pp. 2361-2365). Article 8437312 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/isit.2018.8437312

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title = "The Error Exponent of Generalized Random-Gilbert Varshamov Codes",

abstract = "We introduce a random code construction for channel coding in which the codewords are constrained to be well-separated according to a given distance function, analogously to an existing construction attaining the Gilbert-Varshamov bound. We derive an achievable error exponent for this construction, and prove its tightness with respect to the ensemble average. We show that the exponent recovers the Csisz{\'a}r and K{\"o}rner exponent as a special case by choosing the distance function to be the negative of the empirical mutual information. We further establish the optimality of this distance function with respect to the exponent of the random coding scheme.",

author = "Anelia Somekh-Baruch and Jonathan Scarlett and {Guilleni Fabregas}, Albert",

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Somekh-Baruch, A, Scarlett, J & Guilleni Fabregas, A 2018, The Error Exponent of Generalized Random-Gilbert Varshamov Codes. in 2018 IEEE International Symposium on Information Theory, ISIT 2018., 8437312, IEEE International Symposium on Information Theory - Proceedings, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 2361-2365, 2018 IEEE International Symposium on Information Theory, ISIT 2018, Vail, United States, 17/06/18. https://doi.org/10.1109/isit.2018.8437312

The Error Exponent of Generalized Random-Gilbert Varshamov Codes. / Somekh-Baruch, Anelia; Scarlett, Jonathan; Guilleni Fabregas, Albert.
2018 IEEE International Symposium on Information Theory, ISIT 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 2361-2365 8437312 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We introduce a random code construction for channel coding in which the codewords are constrained to be well-separated according to a given distance function, analogously to an existing construction attaining the Gilbert-Varshamov bound. We derive an achievable error exponent for this construction, and prove its tightness with respect to the ensemble average. We show that the exponent recovers the Csiszár and Körner exponent as a special case by choosing the distance function to be the negative of the empirical mutual information. We further establish the optimality of this distance function with respect to the exponent of the random coding scheme.

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The Error Exponent of Generalized Random-Gilbert Varshamov Codes

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