Regular LDPC codes on BMS wiretap channels: Security bounds

TL;DR

This paper enhances the security guarantees of regular LDPC codes on BMS wiretap channels by reducing information leakage from o(n) to O(log^2 n), advancing the theoretical security bounds.

Contribution

It improves the leakage bounds for LDPC codes on wiretap channels, moving closer to strong security guarantees beyond previous capacity-achieving results.

Findings

Leakage reduced to O(log^2 n)

Improved security bounds for LDPC codes

Advancement beyond previous secrecy guarantees

Abstract

We improve the secrecy guarantees for transmission over general binary memoryless symmetric wiretap channels that relies on regular LDPC codes. Previous works showed that LDPC codes achieve secrecy capacity of some classes of wiretap channels while leaking $o(n)$ bits of information over $n$ uses of the channel. In this note, we improve the security component of these results by reducing the leakage parameter to $O(\log^2 n)$. While this result stops short of proving \emph{strong security}, it goes beyond the general secrecy guarantees derived from properties of capacity-approaching code families.