Regular LDPC codes on BMS wiretap channels: Security bounds

TL;DR

The paper addresses secrecy for transmission over general binary memoryless symmetric wiretap channels using regular LDPC codes. It introduces a Rényi-divergence-based smoothing analysis to bound information leakage and shows that nested Gallager LDPC codes can achieve reliable communication at rates near the secrecy capacity while restricting leakage to $O(\log^2 n)$, a substantial improvement over generic $o(n)$ bounds. The core technique reduces the problem to controlling the output distribution of the eavesdropper by analyzing the LDPC parity-check structure and proving a main $D_{\alpha}$ bound; this yields a near-secrecy-capacity result for the BMS-BSC case and, via channel comparison, extends to general BMS wiretap settings when the eavesdropper’s channel is less capable. Although strong secrecy remains open, the results substantially tighten the leakage bounds for constructive LDPC-based secrecy schemes and clarify how regular LDPC ensembles can approach the secrecy capacity in practical coding scenarios.

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.

Theorems & Definitions (16)

• Remark 1
• Lemma 3.1
• proof
• Proposition 3.2
• Lemma 3.3
• proof
• Theorem 3.4
• proof
• Theorem 3.5
• proof