Finite Blocklength Secrecy Analysis of Polar and Reed-Muller Codes in BEC Semi-Deterministic Wiretap Channels

TL;DR

This paper analyzes the secrecy performance of polar and Reed-Muller codes in a semi-deterministic BEC wiretap channel with short blocklengths, providing bounds and comparisons to second order rates.

Contribution

It is the first work to demonstrate the secrecy performance of these codes in short blocklength regimes for this channel model.

Findings

Reed-Muller codes achieve secrecy rates close to the second order approximation.

Polar codes show a significant gap between achievable rates and second order rates at short blocklengths.

Reed-Muller codes outperform polar codes in the considered setting.

Abstract

In this paper, we consider a semi-deterministic wiretap channel where the main channel is noiseless and the eavesdropper's channel is a binary erasure channel (BEC). We provide a lower bound for the achievable secrecy rates of polar and Reed Muller codes and compare it to the second order coding rate for the semi-deterministic wiretap channel. To the best of our knowledge, this is the first work which demonstrates the secrecy performance of polar and Reed-Muller codes in short blocklengths. The results show that under a total variation secrecy metric, Reed Muller codes can achieve secrecy rates very close to the second order approximation rate. On the other hand, we observe a significant gap between the lower bound for the achievable rates of polar codes and the the second order approximation rate for short blocklengths.