The encode and decode theory of polar code and its performance simulating

Abstract

Based on the channel combination and split, the binary discrete channel will come up a channel polarization phenomenon, when the number of combined channels tends to infinity, part of the channels will become ideal channel without any noise and another part of the channels will became pure noisy channel. The polarization code is a kind of channel coding method based on channel polarization, which can reach Shannon limit in theory. The paper introduced the process of channel polarization, the generations of the generator matrix and the encode method of polar code; besides, it explain a decoding method called succession cancellation, according to any given a GN-cosset code, the estimated received-code can be solved out by calculating each level's LR. Finally, it simulated the channel capacity of polar code under binary erasure channel with MATLAB, as well, it simulated and analyzed d the influence of coding rate for the performance of polar code.