Efficient Multiparty Interactive Coding—Part II: Non-Oblivious Noise

Interactive coding allows two or more parties to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that tolerate a high level of noise while increasing the communication by only a constant factor (i.e., constant rate). In this work (the second part) we provide computationally efficient, constant rate schemes that conduct any computation on arbitrary networks, and succeed with high probability in the presence of adversarial noise that can insert, delete, or alter communicated messages. Our schemes are non-fully-utilized and incur a polynomial (in the size of the network) blowup in the round complexity. Our first scheme resists an oblivious adversary that corrupts at most a fraction $\frac { \varepsilon }{m}$ of the total communication, where $m$ is the number of links in the network and $\varepsilon $ is a small constant. In contrast to the first part of this work, the scheme in this part does not assume that the parties pre-share a long random string. Our second scheme resists an arbitrary (non-oblivious) adversary that corrupts at most a fraction $\frac { \varepsilon }{m\log m}$ of the communication. We further improve the resilience to $\vphantom {\sum ^{R}}\frac { \varepsilon }{m\log \log m}$ by assuming the parties pre-share a long common random $\vphantom {\sum ^{R}}$ string.