On the Bit-Channels for Channel Polarization

Abstract

The problem of constructing polar codes is equivalent to selecting good channels among a set of bit-channels with output alphabet size grows exponentially. To solve the problem, Tal and Vardy proposed a channel quantization algorithm to approximate the original channel by channels with less output symbols. Based on Arıkan’s original work, we derived a matrix form of channel transformation. This formulation automatically merges suitable output symbols, thus reducing the step of preprocessing complexity in Tal and Vardy’s algorithm.