Detecting Symmetrizability in Physical Systems

TL;DR

This paper investigates the computational complexity of detecting symmetrizability in arbitrarily varying channels (AVCs) and introduces efficient algorithms for identifying non-symmetrizable AVCs under certain constraints, aiding in secure wireless communication.

Contribution

It presents a polynomial-time algorithm for determining non-symmetrizability of AVCs, especially under energy constraints, improving understanding of secure data transmission.

Findings

Deciding symmetrizability is non-Turing computable in general.

A polynomial-time algorithm can determine non-symmetrizability with dependence on jammer states.

Energy constraints enable efficient identification of non-symmetrizable AVCs.

Abstract

We study the problem of data transmission under the influence of a jammer, which is typical for wireless systems and commonly modeled as an arbitrarily varying channel (AVC) in information theory. AVC fulfilling a certain set of linear equations are called symmetrizable and are known to be prone to denial of service attacks. Recent work has shown that deciding if a given AVC is symmetrizable or not is a non-Turing computable problem. By relaxing the formulation of symmetrizability, we show the existence of a polynomial-time algorithm that determines whether a given AVC is non-symmetrizable, but displays a critical dependence on the number of jammer input states. We then show how imposing an energy constraint on the jammer allows the same algorithm to efficiently identify large classes of AVCs which are non-symmetrizable.