NDLI: Optimal error rates for interactive coding I: adaptivity and other settings

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Optimal error rates for interactive coding I: adaptivity and other settings

Content Provider	ACM Digital Library
Author	Ghaffari, Mohsen Sudan, Madhu Haeupler, Bernhard
Abstract	We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings. Most significantly, we explore adaptive interactive communication where the communicating parties decide who should speak next based on the history of the interaction. In particular, this decision can depend on estimates of the amount of errors that have occurred so far. Braverman and Rao [STOC'11] show that non-adaptively one can code for any constant error rate below 1/4 but not more. They asked whether this bound could be improved using adaptivity. We answer this open question in the affirmative (with a slightly different collection of resources): Our adaptive coding scheme tolerates any error rate below 2/7 and we show that tolerating a higher error rate is impossible. We also show that in the setting of Franklin et al. [CRYPTO'13], where parties share randomness not known to the adversary, adaptivity increases the tolerable error rate from 1/2 to 2/3. For list-decodable interactive communications, where each party outputs a constant size list of possible outcomes, the tight tolerable error rate is 1/2. Our negative results hold even if the communication and computation are unbounded, whereas for our positive results communication and computations are polynomially bounded. Most prior work considered coding schemes with linear communication bounds, while allowing unbounded computations. We argue that studying tolerable error rates in this relaxed context helps to identify a setting's intrinsic optimal error rate. We set forward a strong working hypothesis which stipulates that for any setting the maximum tolerable error rate is independent of many computational and communication complexity measures. We believe this hypothesis to be a powerful guideline for the design of simple, natural, and efficient coding schemes and for understanding the (im)possibilities of coding for interactive communications.
Starting Page	794
Ending Page	803
Page Count	10
File Format	PDF MP4
ISBN	9781450327107
DOI	10.1145/2591796.2591872
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-05-31
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Adaptivity Error rate Adversarial errors Coding for interactive communication
Content Type	Audio Text
Resource Type	Article

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