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Electrical Engineering Systems Seminar
Speaker: Ori Ohayon
M.Sc. student under the supervision of Prof. Arie Yeredor
Tuesday, 10th June 2025, at 15:00
Room 011, Kitot Building, Faculty of Engineering
Noisy Independent Component Analysis over Galois Fields of Prime Order
Abstract
Independent Component Analysis (ICA) is known as a powerful technique used for the separation of mixed signals. Most of the work done so far in this field focused on the problem formulation over the real R
or complex C
fields, while work on ICA over finite fields focused mostly on the theoretical aspect, and, as far as we know, only for the noiseless case.
The current work presents the basic concepts of the general framework of ICA over finite fields, motivation for real-life applications thereof (such as in Network Coding), and previous work that was done in this framework. We review and characterize random variables over finite fields (specifically over Galois Fields of Prime order GF(P)
) and formulate the associated ICA problem for both the noiseless and the noisy cases.
In the core of this work, we discuss the previously developed AMERICA (Ascending Minimization of EntRopies for ICA) algorithm, and continue to analyze (using a Gaussian approximation) the probability of failure of a modification of AMERICA, which we call WEAK AMERICA, for the noisy model. The probability of failure which we analyze in this work refers to the probability of failing to estimate the inverse of the mixing matrix (up to permutation and scaling of the columns). We present corner cases in which the Central Limit Theorem (CLT) alone fails to provide a reliable approximation and can be improved using the Edgeworth expansion. In addition to the analysis, this work offers a first-of-its-kind semi-blind method to mitigate the effect of the noisy samples for ICA over finite fields. This method of noise mitigation is used in two new algorithms called AMERICANO (AMERICA with NOise) and SWEDEN (SWEeping over Different Estimated Noise parameters).
A special emphasis is placed on the key differences between the noisy and noiseless scenarios, which are reflected in the noisy probability of failure analysis, as well as in the new algorithms and methods for the noisy ICA.
