Date of Original Version

4-2014

Type

Conference Proceeding

Rights Management

© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Abstract or Description

We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any n-round interactive protocol using N rounds over an adversarial channel that corrupts up to ρN transmissions. Important performance measures for a coding scheme are its maximum tolerable error rate ρ, communication complexity N, and computational complexity. We give the first coding scheme for the standard setting which performs optimally in all three measures: Our randomized non-adaptive coding scheme has a near-linear computational complexity and tolerates any error rate δ <; 1/4 with a linear N = Θ(n) communication complexity. This improves over prior results [1]-[4] which each performed well in two of these measures. We also give results for other settings of interest, namely, the first computationally and communication efficient schemes that tolerate ρ <; 2/7 adaptively, ρ <; 1/3 if only one party is required to decode, and ρ <; 1/2 if list decoding is allowed. These are the optimal tolerable error rates for the respective settings. These coding schemes also have near linear computational and communication complexity. These results are obtained via two techniques: We give a general black-box reduction which reduces unique decoding, in various settings, to list decoding. We also show how to boost the computational and communication efficiency of any list decoder to become near linear.

DOI

10.1109/FOCS.2014.49

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Published In

Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 2014, 394-403.