Balancing Communication for Multi-party Interactive Coding

TL;DR

This paper develops a balanced multi-party interactive coding protocol that distributes communication workload evenly among parties while tolerating adversarial errors proportional to the total communication.

Contribution

It introduces a novel mechanism for passing coordination duties among parties, improving load balancing over prior protocols that relied on a single coordinator.

Findings

Achieves constant overhead in total communication despite adversarial errors.

Distributes communication workload evenly among all parties.

Builds upon and improves the protocol of Jain, Kalai, and Lewko.

Abstract

We consider interactive coding in a setting where $n$ parties wish to compute a joint function of their inputs via an interactive protocol over imperfect channels. We assume that adversarial errors can comprise a $\mathcal{O}(\frac{1}{n})$ fraction of the total communication, occurring anywhere on the communication network. Our goal is to maintain a constant multiplicative overhead in the total communication required, as compared to the error-free setting, and also to balance the workload over the different parties. We build upon the prior protocol of Jain, Kalai, and Lewko, but while that protocol relies on a single coordinator to shoulder a heavy burden throughout the protocol, we design a mechanism to pass the coordination duties from party to party, resulting in a more even distribution of communication over the course of the computation.