Interactive Coding with Small Memory

In this work, we design an interactive coding scheme that converts any two party interactive protocol Pi into another interactive protocol Pi', such that even if errors are introduced during the execution of Pi', the parties are able to determine what the outcome of running Pi would be in an error-free setting. Importantly, our scheme preserves the space complexity of the protocol, in addition to the communication and computational complexities. Specifically, if the protocol Pi has communication complexity T, computational complexity t, and space complexity s, the resulting protocol Pi' is resilient to a constant epsilon > 0 fraction of adversarial errors, and has communication complexity approaching T as epsilon approaches 0, computational complexity poly(t), and space complexity O(s log T). Prior to this work, all known interactive coding schemes required the parties to use at least Omega(T) space, as the parties were required to remember the transcript of the conversation thus far, or considered weaker error models.