# Efficient Multiparty Interactive Coding for Insertions, Deletions and Substitutions

## TL;DR

This paper introduces the first efficient multiparty interactive coding scheme resilient to adversarial insertions, deletions, and substitutions, capable of maintaining high communication rates over noisy networks with minimal error.

## Contribution

It presents the first multiparty coding scheme robust to insertions and deletions, extending previous two-party results to arbitrary network topologies.

## Key findings

- Achieves constant rate communication under adversarial noise
- Resilient to a fraction of errors proportional to the number of network links
- First computationally efficient multiparty scheme for insertion-deletion noise

## Abstract

In the field of interactive coding, two or more parties wish to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that can tolerate a high level of noise while increasing the communication by only a constant factor (i.e., constant rate). In this work we consider synchronous communication networks over an arbitrary topology, in the powerful adversarial insertion-deletion noise model. Namely, the noisy channel may adversarially alter the content of any transmitted symbol, as well as completely remove a transmitted symbol or inject a new symbol into the channel. We provide efficient, constant rate schemes that successfully conduct any computation with high probability as long as the adversary corrupts at most $\varepsilon /m$ fraction of the total communication, where $m$ is the number of links in the network and $\varepsilon$ is a small constant. This scheme assumes the parties share a random string to which the adversarial noise is oblivious. We can remove this assumption at the price of being resilient to $\varepsilon / (m\log m)$ adversarial error. While previous work considered the insertion-deletion noise model in the two-party setting, to the best of our knowledge, our scheme is the first multiparty scheme that is resilient to insertions and deletions. Furthermore, our scheme is the first computationally efficient scheme in the multiparty setting that is resilient to adversarial noise.