A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent

Anelia Somekh-Baruch; Jonathan Scarlett; Albert Guillen I. Fabregas

doi:10.1109/isit.2019.8849522

A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent

Anelia Somekh-Baruch, Jonathan Scarlett, Albert Guillen I. Fabregas

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

1 Scopus citations

Abstract

We show that a recursive cost-constrained random coding scheme attains an error exponent that is at least as high as both the random-coding exponent and the expurgated exponent. The random coding scheme enforces that every pair of codewords in the codebook meets a minimum distance condition, and is reminiscent of the Gilbert-Varshamov construction, but with the notable feature of permitting continuous-alphabet channels. The distance function is initially arbitrary, and it is shown that the Chernoff/Bhattacharrya distance suffices to attain the random coding and expurgated exponents.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2938-2942
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/isit.2019.8849522
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Funding

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

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

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10.1109/isit.2019.8849522

Cite this

Somekh-Baruch, A., Scarlett, J., & Fabregas, A. G. I. (2019). A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 2938-2942). Article 8849522 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/isit.2019.8849522

Somekh-Baruch, Anelia ; Scarlett, Jonathan ; Fabregas, Albert Guillen I. / A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent. 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2938-2942 (IEEE International Symposium on Information Theory - Proceedings).

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abstract = "We show that a recursive cost-constrained random coding scheme attains an error exponent that is at least as high as both the random-coding exponent and the expurgated exponent. The random coding scheme enforces that every pair of codewords in the codebook meets a minimum distance condition, and is reminiscent of the Gilbert-Varshamov construction, but with the notable feature of permitting continuous-alphabet channels. The distance function is initially arbitrary, and it is shown that the Chernoff/Bhattacharrya distance suffices to attain the random coding and expurgated exponents.",

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Somekh-Baruch, A, Scarlett, J & Fabregas, AGI 2019, A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849522, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 2938-2942, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/isit.2019.8849522

A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent. / Somekh-Baruch, Anelia; Scarlett, Jonathan; Fabregas, Albert Guillen I.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2938-2942 8849522 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

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

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Somekh-Baruch A, Scarlett J, Fabregas AGI. A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2938-2942. 8849522. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/isit.2019.8849522

A Recursive Cost-Constrained Construction that Attains the Expurgated Exponent

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