Partial Strong Converse for the Non-Degraded Wiretap Channel

TL;DR

This paper establishes a partial strong converse for the non-degraded wiretap channel, showing that exceeding the secrecy capacity results in exponentially vanishing decoding success probability, thus confirming the capacity as a fundamental limit.

Contribution

It proves the partial strong converse for the non-degraded wiretap channel using information spectrum and Chernoff-Cramer bounds, a novel application in this context.

Findings

Exceeding secrecy capacity causes decoding probability to decay exponentially.

The maximum transmission rate remains constant for all error probabilities less than one.

The partial strong converse property holds for the non-degraded wiretap channel.

Abstract

We prove the partial strong converse property for the discrete memoryless \emph{non-degraded} wiretap channel, for which we require the leakage to the eavesdropper to vanish but allow an asymptotic error probability $\epsilon \in [0,1)$ to the legitimate receiver. We show that when the transmission rate is above the secrecy capacity, the probability of correct decoding at the legitimate receiver decays to zero exponentially. Therefore, the maximum transmission rate is the same for $\epsilon \in [0,1)$, and the partial strong converse property holds. Our work is inspired by a recently developed technique based on information spectrum method and Chernoff-Cramer bound for evaluating the exponent of the probability of correct decoding.