TY - GEN

T1 - Interactive error resilience beyond 2/7

AU - Efremenko, Klim

AU - Kol, Gillat

AU - Saxena, Raghuvansh R.

N1 - Publisher Copyright:
© 2020 ACM.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/6/8

Y1 - 2020/6/8

N2 - Interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, Braverman and Rao prove that the maximum error resilience is 1/4 (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the adaptive channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a 2/7 fraction of errors. This was believed to be optimal. We revisit this result, and show how to overcome the 2/7 barrier. Specifically, we show that, over the adaptive channel, every two-party communication protocol can be converted to a protocol that is resilient to 7/24 > 2/7 fraction of errors with only a constant multiplicative overhead to the total communication. The protocol is obtained by a novel implementation of a feedback mechanism over the adaptive channel.

AB - Interactive error correcting codes can protect interactive communication protocols against a constant fraction of adversarial errors, while incurring only a constant multiplicative overhead in the total communication. What is the maximum fraction of errors that such codes can protect against? For the non-adaptive channel, where the parties must agree in advance on the order in which they communicate, Braverman and Rao prove that the maximum error resilience is 1/4 (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the adaptive channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a 2/7 fraction of errors. This was believed to be optimal. We revisit this result, and show how to overcome the 2/7 barrier. Specifically, we show that, over the adaptive channel, every two-party communication protocol can be converted to a protocol that is resilient to 7/24 > 2/7 fraction of errors with only a constant multiplicative overhead to the total communication. The protocol is obtained by a novel implementation of a feedback mechanism over the adaptive channel.

KW - Communication Complexity

KW - Error Resilience

KW - Interactive Coding

UR - http://www.scopus.com/inward/record.url?scp=85086764027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85086764027&partnerID=8YFLogxK

U2 - 10.1145/3357713.3384320

DO - 10.1145/3357713.3384320

M3 - Conference contribution

AN - SCOPUS:85086764027

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 565

EP - 578

BT - STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Makarychev, Konstantin

A2 - Makarychev, Yury

A2 - Tulsiani, Madhur

A2 - Kamath, Gautam

A2 - Chuzhoy, Julia

PB - Association for Computing Machinery

T2 - 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020

Y2 - 22 June 2020 through 26 June 2020

ER -