Information Spectrum Approach to Strong Converse Theorems for Degraded Wiretap Channels

TL;DR

This paper uses the information spectrum method to establish the partial strong converse property for degraded wiretap channels, showing the maximum transmission rate is unaffected by the error probability threshold.

Contribution

It introduces a general information spectrum approach to prove the partial strong converse property for various classes of wiretap channels, including non-stationary ones.

Findings

Maximum rate is independent of error probability threshold for degraded wiretap channels.

Provides necessary and sufficient conditions for the partial strong converse property.

Extends results to non-stationary symmetric and degraded wiretap channels.

Abstract

We consider block codes for degraded wiretap channels in which the legitimate receiver decodes the message with an asymptotic error probability no larger than $\varepsilon$ but the leakage to the eavesdropper vanishes. For discrete memoryless and Gaussian wiretap channels, we show that the maximum rate of transmission does not depend on $\varepsilon\in [0,1)$, i.e., such channels possess the partial strong converse property. Furthermore, we derive sufficient conditions for the partial strong converse property to hold for memoryless but non-stationary symmetric and degraded wiretap channels. Our proof techniques leverage the information spectrum method, which allows us to establish a necessary and sufficient condition for the partial strong converse to hold for general wiretap channels without any information stability assumptions.