On Interactive Coding Schemes with Adaptive Termination

TL;DR

This paper investigates how adaptive termination in interactive coding schemes can improve error resilience, allowing parties to end protocols early and potentially enhance robustness against adversarial errors.

Contribution

It introduces the concept of adaptive termination in interactive coding and analyzes its impact on error resilience in message exchange protocols.

Findings

Adaptive termination can increase error resilience in interactive coding.

Partially adaptive schemes outperform non-adaptive ones under certain conditions.

Early termination strategies improve robustness against adversarial errors.

Abstract

In interactive coding, Alice and Bob wish to compute some function $f$ of their individual private inputs $x$ and $y$. They do this by engaging in an interactive protocol to jointly compute $f(x,y)$. The goal is to do this in an error-resilient way, such that even given some fraction of adversarial corruptions to the protocol, both parties still learn $f(x,y)$. Typically, the error resilient protocols constructed by interactive coding schemes are \emph{non-adaptive}, that is, the length of the protocol as well as the speaker in each round is fixed beforehand. The maximal error resilience obtainable by non-adaptive schemes is now well understood. In order to circumvent known barriers and achieve higher error resilience, the work of Agrawal, Gelles, and Sahai (ISIT 2016) introduced to interactive coding the notion of \emph{adaptive} schemes, where the length of the protocol or the speaker order are no longer necessarily fixed. In this paper, we study the power of \emph{adaptive termination} in the context of the error resilience of interactive coding schemes. In other words, what is the power of schemes where Alice and Bob are allowed to disengage from the protocol early? We study this question in two contexts, both for the task of \emph{message exchange}, where the goal is to learn the other party's input.