Rate-Equivocation Optimal Spatially Coupled LDPC Codes for the BEC Wiretap Channel

TL;DR

This paper demonstrates that spatially coupled LDPC codes based on convolutional ensembles can achieve the full rate-equivocation region for the BEC wiretap channel, leveraging the threshold saturation phenomenon.

Contribution

It introduces a regular two-edge type convolutional LDPC ensemble construction that achieves optimal secrecy performance on the BEC wiretap channel.

Findings

Achieves the entire rate-equivocation region for the BEC wiretap channel.

Utilizes spatial coupling to convert MAP thresholds into BP thresholds.

Conjectures universality for binary memoryless symmetric channels with degraded wiretapper channels.

Abstract

We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We use convolutional LDPC ensembles based on the coset encoding scheme. More precisely, we consider regular two edge type convolutional LDPC ensembles. We show that such a construction achieves the whole rate-equivocation region of the BEC wiretap channel. Convolutional LDPC ensemble were introduced by Felstr\"om and Zigangirov and are known to have excellent thresholds. Recently, Kudekar, Richardson, and Urbanke proved that the phenomenon of "Spatial Coupling" converts MAP threshold into BP threshold for transmission over the BEC. The phenomenon of spatial coupling has been observed to hold for general binary memoryless symmetric channels. Hence, we conjecture that our construction is a universal rate-equivocation achieving construction when the main channel and wiretapper's channel are binary memoryless symmetric channels, and the wiretapper's channel is degraded with respect to the main channel.