Interactive Coding with Small Memory and Improved Rate

In this work, we study two-party interactive coding for adversarial noise, when both parties have limited memory. We show how to convert any adaptive protocol Π into a protocol Π' that is robust to an ε-fraction of adversarial corruptions, not too much longer than Π, and which uses small space. More precisely, if Π requires space log(s) and has |Π| rounds of communication, then Π' requires O_ε(log s log |Π|) memory, and has |Π'| = |Π|·( 1 + O( √ ε log log 1/ε )) rounds of communication. The above matches the best known communication rate, even for protocols with no space restrictions.