Independent Component Analysis over Galois fields of prime order

Arie Yeredor*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


We consider the framework of Independent Component Analysis (ICA) for the case where the independent sources and their linear mixtures all reside in a Galois field of prime order P. Similarities and differences from the classical ICA framework (over the real field) are explored. We show that a necessary and sufficient identifiability condition is that none of the sources should have a uniform distribution. We also show that pairwise independence of the mixtures implies their full mutual independence (namely a nonmixing condition) in the binary (P=2) and ternary (P=3) cases, but not necessarily in higher order (P>3) cases. We propose two different iterative separation (or identification) algorithms: One is based on sequential identification of the smallest-entropy linear combinations of the mixtures and is shown to be equivariant with respect to the mixing matrix; the other is based on sequential minimization of the pairwise mutual information measures. We provide some basic performance analysis for the binary (P=2) case, supplemented by simulation results for higher orders, demonstrating advantages and disadvantages of the proposed separation approaches.

Original languageEnglish
Article number5961799
Pages (from-to)5342-5359
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2011


  • Blind source separation (BSS)
  • Galois fields
  • TomlinsonHarashima precoding
  • entropy minimization
  • finite fields
  • independent component analysis (ICA)


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