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|Abstract:||Interactive error correcting codesInteractive 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 /2 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.|
|Citation:||Efremenko, Klim, Gillat Kol, and Raghuvansh R. Saxena. "Binary Interactive Error Resilience Beyond 1/8 (or why (1/2)^3>1/8)." In IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) (2020): pp. 470-481. doi:10.1109/FOCS46700.2020.00051|
|Pages:||470 - 481|
|Type of Material:||Conference Article|
|Journal/Proceeding Title:||IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)|
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