Interactive Communication for Data Exchange

TL;DR

This paper introduces a new interactive protocol for data exchange, providing tight bounds on the communication needed and demonstrating the advantages of interaction over non-interactive methods.

Contribution

It develops a single-shot analysis relating data exchange to secret key agreement, deriving asymptotically tight bounds and characterizing the optimal communication rate with interaction.

Findings

Interactive protocol increases communication efficiency

Bounds are asymptotically tight for general discrete variables

Interaction reduces communication length compared to non-interactive methods

Abstract

Two parties observing correlated data seek to exchange their data using interactive communication. How many bits must they communicate? We propose a new interactive protocol for data exchange which increases the communication size in steps until the task is done. Next, we derive a lower bound on the minimum number of bits that is based on relating the data exchange problem to the secret key agreement problem. Our single-shot analysis applies to all discrete random variables and yields upper and lower bound of a similar form. In fact, the bounds are asymptotically tight and lead to a characterization of the optimal rate of communication needed for data exchange for a general sequence such as mixture of IID random variables as well as the optimal second-order asymptotic term in the length of communication needed for data exchange for the IID random variables, when the probability of error is fixed. This gives a precise characterization of the asymptotic reduction in the length of optimal communication due to interaction; in particular, two-sided Slepian-Wolf compression is strictly suboptimal.