Towards coding for maximum errors in interactive communication

Abstract

We show that it is possible to encode any communication protocol between two parties so that the protocol succeeds even if a (1/4 − ǫ) fraction of all symbols transmitted by the parties are corrupted adversarially, at a cost of increasing the communication in the protocol by a constant factor (the constant depends on epsilon). This encoding uses a constant sized alphabet. This improves on an earlier result of Schulman, who showed how to recover when the fraction of errors is bounded by 1/240. We also show how to simulate an arbitrary protocol with a protocol using the binary alphabet, a constant factor increase in communication and tolerating a 1/8 − ǫ fraction of errors.

Optimal Coding for Streaming Authentication and Interactive Communication

“…We also show that for higher noise rates, no constant-rate interactive protocol exists for tasks that depend on inputs of both parties. Similarly to previous results for interactive communication with adversarial noise [24,5,9], our decoding scheme is inefficient. Very recently, Brakerski and Kalai [2] showed how to augment previous results of interactive communication protocols and achieved efficient schemes that withstand adversarial noise (the computation efficiency was further improved by Brakerski and Naor [3] to O (N log N )).…”

“…In the interactive communication scenario, two parties perform an arbitrary interactive protocol over a noisy channel, while keeping the amount of exchanged data only a constant factor more than an equivalent protocol for a noiseless channel (i.e., the encoding is constant-rate). This question was initially considered for both random and adversarial noise by Schulman [22,23,24] who showed a constantrate encoding scheme that copes with a noise rate of up to 1/240, and recently revisited by Braverman and Rao [5] who showed how to deal with noise rates less than 1/4. In addition, Braverman and Rao show that 1/4 is the highest error rate any protocol can withstand, as long as the protocol defines whose turn it is to speak at every round regardless of the observed noise.…”

“…In this work we improve the bound obtained by [5] by allowing the parties to pre-share a secret key. Specifically, we show how to convert any interactive protocol (for noiseless channel) into a constant-rate protocol that withstands any adversarial noise level smaller than 1/2, given pre-shared randomness.…”

Efficient and Explicit Coding for Interactive Communication

“…Also, another result we obtain relates to the recent work of Braverman and Rao [7]. They give a new simulation procedure, again based on absolute tree codes, which uses a constant-sized alphabet and succeeds against an adversarial channel as long as the fraction of errors is at most 1/4− (the simulation tolerates a 1/8− error fraction when using a binary alphabet).…”

“…In a recent paper [7] Braverman and Rao show how to simulate any 2-party protocol over an adversarial channel, as long as the fraction of errors is at most 1/4 − 2 , for any constant 2 > 0. Their simulation is also based on absolute tree codes.…”