Binary Interactive Error Resilience Beyond 1/8 (or why (½)3>1/8)

Klim Efremenko; Gillat Kol; Raghuvansh Saxena

Binary Interactive Error Resilience Beyond 1/8 (or why (½)³>1/8)

Klim Efremenko, Gillat Kol, Raghuvansh Saxena

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Book/Report › Report › peer-review

Abstract

Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that such codes can protect against? If the error-resilient protocol is allowed to communicate large (constant sized) symbols, Braverman and Rao (STOC, 2011) show that the maximum rate of corruptions that can be tolerated is 1/4. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to 1/8 fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the 1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to 5/39 > 1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.

Original language	American English
Number of pages	1
State	Published - 9 Apr 2021

Keywords

Interactive Coding
communication complexity

Access to Document

https://eccc.weizmann.ac.il/report/2021/051

Cite this

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abstract = "Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that such codes can protect against? If the error-resilient protocol is allowed to communicate large (constant sized) symbols, Braverman and Rao (STOC, 2011) show that the maximum rate of corruptions that can be tolerated is 1/4. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to 1/8 fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the 1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to 5/39 > 1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.",

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N2 - Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that such codes can protect against? If the error-resilient protocol is allowed to communicate large (constant sized) symbols, Braverman and Rao (STOC, 2011) show that the maximum rate of corruptions that can be tolerated is 1/4. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to 1/8 fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the 1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to 5/39 > 1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.

AB - Interactive error correcting codes are codes that encode a two party communication protocol to an error-resilient protocol that succeeds even if a constant fraction of the communicated symbols are adversarially corrupted, at the cost of increasing the communication by a constant factor. What is the largest fraction of corruptions that such codes can protect against? If the error-resilient protocol is allowed to communicate large (constant sized) symbols, Braverman and Rao (STOC, 2011) show that the maximum rate of corruptions that can be tolerated is 1/4. They also give a binary interactive error correcting protocol that only communicates bits and is resilient to 1/8 fraction of errors, but leave the optimality of this scheme as an open problem. We answer this question in the negative, breaking the 1/8 barrier. Specifically, we give a binary interactive error correcting scheme that is resilient to 5/39 > 1/8 fraction of adversarial errors. Our scheme builds upon a novel construction of binary list-decodable interactive codes with small list size.

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