Explicit Capacity Approaching Coding for Interactive Communication

Ran Gelles, Bernhard Haeupler, Gillat Kol, Noga Ron-Zewi, Avi Wigderson

Research output: Contribution to journalArticlepeer-review

Abstract

We show an explicit (that is, efficient and deterministic) capacity approaching interactive coding scheme that simulates any interactive protocol under random errors with nearly optimal communication rate. Specifically, over the binary symmetric channel with crossover probability ∈, our coding scheme achieves a communication rate of 1 - O(√H(∈)), together with negligible exp (-Ω (∈4 n/n)) failure probability (over the randomness of the channel). A rate of 1 - Θ (√H(∈)) is likely asymptotically optimal as a result of Kol and Raz (2013) suggests. Prior to this paper, such a communication rate was achievable only using randomized coding schemes [Kol and Raz (2013); Hauepler (2014)].

Original languageEnglish
Article number8345651
Pages (from-to)6546-6560
Number of pages15
JournalIEEE Transactions on Information Theory
Volume64
Issue number10
DOIs
StatePublished - Oct 2018

Bibliographical note

Funding Information:
R. Gelles was supported in part by NSF under Grant CCF-1149888 and in part by the Israel Science Foundation under Grant 1078/17. B. Haeupler was supported in part by the NSF under Grant CCF- 1527110 and Grant CCF-1618280, and in part by the NSF CAREER award under Grant CCF-1750808. G. Kol was supported in part by the Fund for Math and in part by the Weizmann Institute of Science National Post-Doctoral Award Program for Advancing Women in Science. N. Ron-Zewi was supported in part by NSF under Grant CCF-1412958 and Grant CCF- 1445755, in part by a Rothschild fellowship, and in part by an Alon fellowship. A. Wigderson was supported by the NSF under Grant CCF-1412958.

Funding Information:
Manuscript received April 26, 2017; revised January 18, 2018; accepted April 2, 2018. Date of publication April 24, 2018; date of current version September 13, 2018. R. Gelles was supported in part by NSF under Grant CCF-1149888 and in part by the Israel Science Foundation under Grant 1078/17. B. Haeupler was supported in part by the NSF under Grant CCF-1527110 and Grant CCF-1618280, and in part by the NSF CAREER award under Grant CCF-1750808. G. Kol was supported in part by the Fund for Math and in part by the Weizmann Institute of Science National PostDoctoral Award Program for Advancing Women in Science. N. Ron-Zewi was supported in part by NSF under Grant CCF-1412958 and Grant CCF-1445755, in part by a Rothschild fellowship, and in part by an Alon fellowship. A. Wigderson was supported by the NSF under Grant CCF-1412958. This paper was presented at the 2016 Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms.

Publisher Copyright:
© 2018 IEEE.

Keywords

  • Interactive communication
  • coding protocols
  • deterministic interactive coding
  • tree codes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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