A Lattice Coding Scheme for Secret Key Generation from Gaussian Markov Tree Sources

TL;DR

This paper proposes a nested lattice coding scheme for secret key generation from Gaussian sources arranged in a Markov tree, analyzing its rate and optimality in different quantization limits.

Contribution

It introduces a polynomial-complexity lattice-based scheme for secret key generation in Gaussian Markov tree sources and characterizes its achievable rate and optimality conditions.

Findings

Scheme achieves optimal rate in fine quantization limit for some cases

Scheme's computational complexity is polynomial in sample size

Not always optimal in the limit of fine quantization

Abstract

In this article, we study the problem of secret key generation in the multiterminal source model, where the terminals have access to correlated Gaussian sources. We assume that the sources form a Markov chain on a tree. We give a nested lattice-based key generation scheme whose computational complexity is polynomial in the number, N , of independent and identically distributed samples observed by each source. We also compute the achievable secret key rate and give a class of examples where our scheme is optimal in the fine quantization limit. However, we also give examples that show that our scheme is not always optimal in the limit of fine quantization.