A Comparison of Skewed and Orthogonal Lattices in Gaussian Wiretap Channels

TL;DR

This paper compares skewed and orthogonal lattices in Gaussian wiretap channels, showing orthogonal lattices are suboptimal for secure communication despite simple labeling.

Contribution

It provides a rigorous analysis demonstrating the suboptimality of orthogonal lattices compared to skewed lattices in wiretap channel coding.

Findings

Orthogonal lattices are suboptimal for both error and security performance.

Skewed lattices outperform orthogonal lattices in Gaussian wiretap channels.

Simple bit labeling does not compensate for the suboptimality of orthogonal lattices.

Abstract

We consider lattice coset-coded transmissions over a wiretap channel with additive white Gaussian noise (AWGN). Examining a function that can be interpreted as either the legitimate receiver's error probability or the eavesdropper's correct decision probability, we rigorously show that, albeit offering simple bit labeling, orthogonal nested lattices are suboptimal for coset coding in terms of both the legitimate receiver's and the eavesdropper's probabilities.