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Paper Detail

Paper Title On the Convergence of the Polarization Process in the Noisiness/Weak-* Topology
Paper IdentifierTH3.R2.3
Authors Rajai Nasser, American University of Beirut, Lebanon
Session Polarization
Location Saint Germain, Level 3
Session Time Thursday, 11 July, 14:30 - 16:10
Presentation Time Thursday, 11 July, 15:10 - 15:30
Manuscript  Click here to download the manuscript
Abstract Let W be a channel where the input alphabet is endowed with an Abelian group operation, and let (W_n)_{n>=0} be Arıkan's channel-valued polarization process that is obtained from W using this operation. We prove that the process (W_n)_{n>=0} converges almost surely to deterministic homomorphism channels in the noisiness/weak-* topology. This provides a simple proof of multilevel polarization for a large family of channels, containing among others, discrete memoryless channels (DMC), and channels with continuous output alphabets. This also shows that any continuous channel functional converges almost surely (even if it does not induce a submartingale or a supermartingale).