Finite-blocklength performance of polar wiretap codes under a total variation secrecy constraint

TL;DR

This paper analyzes the finite-blocklength performance of polar wiretap codes under a total variation secrecy constraint, providing bounds and design criteria for secure communication.

Contribution

It introduces a new TVD-based secrecy criterion and derives finite blocklength bounds for polar wiretap codes over a binary erasure channel.

Findings

Leakage bounded by sum of TVDs of bit-channels

New asymptotic design criterion for vanishing TVD leakage

Finite blocklength lower bounds for secrecy rate

Abstract

We study the performance of polarizing codes over a degraded symmetric wiretap channel under a total variation distance (TVD) secrecy constraint. We show that the leakage can be bounded by the sum of the TVDs of the bit-channels corresponding to the confidential and frozen bits. In the asymptotic regime, this gives a new criterion to design wiretap codes with vanishing TVD leakage. In finite blocklength, it allows us to compute lower bounds for the secrecy rate of different families of polarizing wiretap codes over a binary erasure wiretap channel.