Properties of the Polarization Transformations for the Likelihood Ratios of Symmetric B-DMCs

In this paper we investigate, starting with a symmetric B-DMC, the evolution of various probabilities of the likelihood ratios of the synthetic channels created by the recursive application of the basic polarization transformations. The analysis provides a new perspective into the theory of channel polarization initiated by Ar{\i}kan and helps us to address a problem related to approximating the computations of the likelihood ratios of the synthetic channels.