  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 non-mixing 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.
