69,339 research outputs found
Interactive Channel Capacity Revisited
We provide the first capacity approaching coding schemes that robustly
simulate any interactive protocol over an adversarial channel that corrupts any
fraction of the transmitted symbols. Our coding schemes achieve a
communication rate of over any
adversarial channel. This can be improved to for
random, oblivious, and computationally bounded channels, or if parties have
shared randomness unknown to the channel.
Surprisingly, these rates exceed the interactive channel capacity bound
which [Kol and Raz; STOC'13] recently proved for random errors. We conjecture
and to be the optimal rates for their respective settings
and therefore to capture the interactive channel capacity for random and
adversarial errors.
In addition to being very communication efficient, our randomized coding
schemes have multiple other advantages. They are computationally efficient,
extremely natural, and significantly simpler than prior (non-capacity
approaching) schemes. In particular, our protocols do not employ any coding but
allow the original protocol to be performed as-is, interspersed only by short
exchanges of hash values. When hash values do not match, the parties backtrack.
Our approach is, as we feel, by far the simplest and most natural explanation
for why and how robust interactive communication in a noisy environment is
possible
Interactive Coding Resilient to an Unknown Number of Erasures
We consider distributed computations between two parties carried out over a noisy channel that may erase messages. Following a noise model proposed by Dani et al. (2018), the noise level observed by the parties during the computation in our setting is arbitrary and a priori unknown to the parties.
We develop interactive coding schemes that adapt to the actual level of noise and correctly execute any two-party computation. Namely, in case the channel erases T transmissions, the coding scheme will take N+2T transmissions using an alphabet of size 4 (alternatively, using 2N+4T transmissions over a binary channel) to correctly simulate any binary protocol that takes N transmissions assuming a noiseless channel. We can further reduce the communication to N+T by relaxing the communication model and allowing parties to remain silent rather than forcing them to communicate in every round of the coding scheme.
Our coding schemes are efficient, deterministic, have linear overhead both in their communication and round complexity, and succeed (with probability 1) regardless of the number of erasures T
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