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TR20-022 | 19th February 2020 21:21

Interactive Error Resilience Beyond $\frac{2}{7}$


Authors: Klim Efremenko, Gillat Kol, Raghuvansh Saxena
Publication: 22nd February 2020 04:29
Downloads: 124


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~$\frac{1}{4}$ (STOC, 2011). Ghaffari, Haeupler, and Sudan (STOC, 2014) consider the {\em adaptive} channel, where the order in which the parties communicate may not be fixed, and give a clever protocol that is resilient to a $\frac{2}{7}$ fraction of errors. This was believed to be optimal.

We revisit this result, and show how to overcome the $\frac{2}{7}$ barrier. Specifically, we show that, over the adaptive channel, every two-party communication protocol can be converted to a protocol that is resilient to $\frac{7}{24} > \frac{2}{7}$ 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.

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