On Capacities of the Two-User Union Channel with Complete Feedback

Zilin Jiang; Nikita Polyanskii; Ilya Vorobyev

doi:10.1109/TIT.2018.2889250

On Capacities of the Two-User Union Channel with Complete Feedback

Zilin Jiang, Nikita Polyanskii, Ilya Vorobyev

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The exact values of the optimal symmetric rate point in the Cover-Leung capacity region of the two-user union channel with complete feedback were determined by Willems when the size of the input alphabet is 2, and by Vinck et al. when the size is at least 6. We complete this line of research when the size of the input alphabet is 3, 4, or 5. The proof hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality. For the zero-error capacity region, using superposition coding, we provide a practical near-optimal communication scheme which improves all the previous explicit constructions.

Original language	English (US)
Article number	8586908
Pages (from-to)	2774-2781
Number of pages	8
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2018.2889250
State	Published - May 2019
Externally published	Yes

Keywords

Union channel
channel capacity
entropy function
feedback
zero-error capacity

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2018.2889250

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title = "On Capacities of the Two-User Union Channel with Complete Feedback",

abstract = "The exact values of the optimal symmetric rate point in the Cover-Leung capacity region of the two-user union channel with complete feedback were determined by Willems when the size of the input alphabet is 2, and by Vinck et al. when the size is at least 6. We complete this line of research when the size of the input alphabet is 3, 4, or 5. The proof hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality. For the zero-error capacity region, using superposition coding, we provide a practical near-optimal communication scheme which improves all the previous explicit constructions.",

keywords = "Union channel, channel capacity, entropy function, feedback, zero-error capacity",

author = "Zilin Jiang and Nikita Polyanskii and Ilya Vorobyev",

note = "Funding Information: Manuscript received April 23, 2018; revised September 22, 2018; accepted November 27, 2018. Date of publication December 24, 2018; date of current version April 19, 2019. Z. Jiang was supported by the Israel Science Foundation (ISF) under Grant 1162/15 and Grant 936/16. N. Polyanskii was supported in part by ISF under Grant 1162/15 and Grant 326/17 and in part by the Russian Foundation for Basic Research (RFBR) under Grant 16-01-00440 A, Grant 18-07-01427 A, and Grant 18-31-00310 MOL_A. I. Vorobyev was supported by RFBR under Grant 16-01-00440 A, Grant 18-07-01427 A, and Grant 18-31-00361 MOL_A. Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2019",

month = may,

doi = "10.1109/TIT.2018.2889250",

language = "English (US)",

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AU - Vorobyev, Ilya

N1 - Funding Information: Manuscript received April 23, 2018; revised September 22, 2018; accepted November 27, 2018. Date of publication December 24, 2018; date of current version April 19, 2019. Z. Jiang was supported by the Israel Science Foundation (ISF) under Grant 1162/15 and Grant 936/16. N. Polyanskii was supported in part by ISF under Grant 1162/15 and Grant 326/17 and in part by the Russian Foundation for Basic Research (RFBR) under Grant 16-01-00440 A, Grant 18-07-01427 A, and Grant 18-31-00310 MOL_A. I. Vorobyev was supported by RFBR under Grant 16-01-00440 A, Grant 18-07-01427 A, and Grant 18-31-00361 MOL_A. Publisher Copyright: © 1963-2012 IEEE.

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AB - The exact values of the optimal symmetric rate point in the Cover-Leung capacity region of the two-user union channel with complete feedback were determined by Willems when the size of the input alphabet is 2, and by Vinck et al. when the size is at least 6. We complete this line of research when the size of the input alphabet is 3, 4, or 5. The proof hinges on the technical lemma that concerns the maximal joint entropy of two independent random variables in terms of their probability of equality. For the zero-error capacity region, using superposition coding, we provide a practical near-optimal communication scheme which improves all the previous explicit constructions.

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On Capacities of the Two-User Union Channel with Complete Feedback

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Keywords

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