Simulating Noisy Channel Interaction

TL;DR

This paper demonstrates that interaction over a noisy binary symmetric channel can be efficiently simulated over a noiseless channel, introduces an energy cost model, and explores the relationship between energy and information complexity.

Contribution

It provides a novel simulation method for noisy channels using noiseless channels and introduces an energy cost model linked to information complexity.

Findings

Simulation of noisy channels with O(ε^2 T) rounds over noiseless channels

Energy cost model equivalent to external information complexity

Self-reduction technique for simulating less-noisy channels

Abstract

We show that $T$ rounds of interaction over the binary symmetric channel $BSC_{1/2-\epsilon}$ with feedback can be simulated with $O(\epsilon^2 T)$ rounds of interaction over a noiseless channel. We also introduce a more general "energy cost" model of interaction over a noisy channel. We show energy cost to be equivalent to external information complexity, which implies that our simulation results are unlikely to carry over to energy complexity. Our main technical innovation is a self-reduction from simulating a noisy channel to simulating a slightly-less-noisy channel, which may have other applications in the area of interactive compression.