Abstract-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 1 − O( log log 1/ ) over any adversarial channel. This can be improved to 1 − O( √ ) for random, oblivious, and computationally bounded channels, or if parties have shared randomness unknown to the channel. Surprisingly, these rates exceed the 1 − Ω( H( )) = 1 − Ω( log 1/ ) interactive channel capacity bound which [Kol and Raz; STOC'13] recently proved for random errors. We conjecture 1 − Θ( log log 1/ ) and 1 − Θ( √ ) 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.
When the noise is adversarial rather than random, the slowdown increases to 1 + O( ε log log 1/ε) REF .
Interactive Channel Capacity Revisited
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
Mathematics Computer Science