Achievability of nearly-exact alignment for correlated Gaussian databases

Osman Emre Dai, Daniel Cullina, Negar Kiyavash

Abstract: We study the conditions that allow for the alignment of correlated databases with multivariate Gaussian features. We present some analysis tools that allow us to go beyond the achievability result for exact alignment and derive the condition for nearly-exact alignment. Our main theorem gives an expression for the order of magnitude of the error in alignment as a function of mutual information between features.