Applications of LDPC Codes to the Wiretap Channel

TL;DR

This paper explores the use of LDPC codes for secure communication over wiretap channels, demonstrating capacity-achieving codes and practical constructions for various channel types, including binary erasure and symmetric channels.

Contribution

It provides an alternative proof of secrecy capacity and introduces LDPC-based codes that achieve or approach this capacity for wiretap channels.

Findings

LDPC codes can achieve secrecy capacity in wiretap channels.

Practical LDPC-based codes are designed for binary erasure and symmetric channels.

Linear-time decodable secrecy codes are constructed for specific channel models.

Abstract

With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channels. We provide an alternative view of the proof for secrecy capacity of wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide security at rates below secrecy capacity. For the special case of a noiseless main channel and binary erasure channel, we consider encoder and decoder design for codes achieving secrecy on the wiretap channel; we show that it is possible to construct linear-time decodable secrecy codes based on LDPC codes that achieve secrecy.