Interference Channels with Strong Secrecy

TL;DR

This paper investigates the impact of a 1-bit information leakage on secrecy measures in interference channels, demonstrating that strong secrecy can be achieved with nested lattice codes using a single lattice point, outperforming previous methods.

Contribution

It proves that strong secrecy is achievable with nested lattice codes using a single lattice point, enhancing secrecy speed and efficiency compared to prior approaches.

Findings

Strong secrecy can be achieved with a single lattice point.

Nested lattice codes outperform Gaussian codes under strong secrecy.

Secrecy decreases faster with the new coding scheme.

Abstract

It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this 1 bit information on the equivocation expressed in three commonly used information theoretic measures, i.e., the Shannon entropy, the Renyi entropy and the min entropy. We then demonstrate its applications in an interference channel with a confidential message. In our previous work, we showed that nested lattice codes can outperform Gaussian codes for this channel when the achieved rate is measured with the weak secrecy notion. Here, with the Renyi entropy and the min entropy measure, we prove that the same secure degree of freedom is achievable with the strong secrecy notion as well. A major benefit of the new coding scheme is that the strong secrecy is generated from a single lattice point instead of a sequence of lattice points. Hence the mutual information between the confidential message and the observation of the eavesdropper decreases much faster with the number of channel uses than previously known strong secrecy coding methods for nested lattice codes.