Explicit Capacity Approaching Coding for Interactive Communication

We show an <italic>explicit</italic> (that is, efficient and deterministic) capacity approaching interactive coding scheme that simulates any interactive protocol under random errors with nearly optimal communication rate. Specifically, over the binary symmetric channel with crossover probability <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>, our coding scheme achieves a communication rate of <inline-formula> <tex-math notation="LaTeX">$1 - O(\sqrt {H({\epsilon })})$ </tex-math></inline-formula>, together with negligible <inline-formula> <tex-math notation="LaTeX">$\exp (-\Omega (\epsilon ^{4}\,\,n/\log n))$ </tex-math></inline-formula> failure probability (over the randomness of the channel). A rate of <inline-formula> <tex-math notation="LaTeX">$1 - \tilde \Theta (\sqrt {H({\epsilon })})$ </tex-math></inline-formula> is likely asymptotically optimal as a result of Kol and Raz (2013) suggests. Prior to this paper, such a communication rate was achievable only using <italic>randomized</italic> coding schemes [Kol and Raz (2013); Hauepler (2014)].

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