Blind Separation of Noisy Mixtures Over Galois Fields

Abstract

We consider the blind separation of noisy mixtures of independent sources over a finite field. Namely, the source signals, the elements of the mixing matrix, the noise signals, the noisy output signals and the associated arithmetic operations all reside in a finite (Galois) field. The source signals are assumed to be mutually independent and temporally stationary with unknown probability distributions, and the goal is to estimate the unknown mixing matrix based on the observed (noise-contaminated) output signals only. Previous work on this problem only considered the noiseless case, and several separation approaches have been proposed. In this work we address the more challenging noisy case, where we assume that each of the observed mixture signals is contaminated by independent additive noise (over the field), reflected by occasional symbol errors. To this end, we propose a modification of the "Ascending Minimization of EntRopies for ICA" ("AMERICA") algorithm. The modified version (dubbed "AMERICANO" - "AMERICA" with NOise) accounts for the noise through mitigation of the empirical characteristic tensor of the observations. We demonstrate the loss of equivariance inflicted on AMERICA by the noise, as well as the resulting improvement by AMERICANO.