Inducing information stability and applications thereof to obtaining information theoretic necessary conditions directly from operational requirements

TL;DR

This paper introduces a new method to derive information theoretic necessary conditions directly from operational requirements, demonstrated through applications to authentication and wiretap channels.

Contribution

It presents a novel construction for information stability and a methodology to obtain necessary conditions from operational constraints, advancing information theory techniques.

Findings

Derived new necessary conditions for keyed authentication.

Established the capacity region of the wiretap channel with finite leakage.

Demonstrated the methodology's usefulness through practical examples.

Abstract

This work constructs a discrete random variable that, when conditioned upon, ensures information stability of quasi-images. Using this construction, a new methodology is derived to obtain information theoretic necessary conditions directly from operational requirements. In particular, this methodology is used to derive new necessary conditions for keyed authentication over discrete memoryless channels and to establish the capacity region of the wiretap channel, subject to finite leakage and finite error, under two different secrecy metrics. These examples establish the usefulness of the proposed methodology.