Channel Polarization: A Method for Constructing Capacity-Achieving Codes

Abstract

According to Shannon's Theorem, the possible code rate of a noisy channel is limited by the channel capacity; and there exist coding methods that could achieve the capacity of noisy channels. A method, called channel polarization (or polar coding), proposed by Erdal Arikan, was the first one mathematically proved to be capacity-achieving for symmetric binary-input discrete memoryless channels (B-DMC). In this project, the algorithm of this polar coding method was studied, and a simulation package was produced to evaluate its performance. Channels including Binary Erasure Channel (BEC), Binary Symmetric Channel (BSC) and Additive White Gaussian Noise channel (AWGN) were assumed in the simulation. As shown by the simulation results, for a give coding block length N=2n the polar coding method re-allocated the capacities over the channels, so that the equivalent channel capacities at different bit locations polarized as the coding block length becomes large; and the block error rate obtained in the simulation agreed with the bound given by Erdal Arikan in his paper. These results supported the capacity-achieving performance of the polar coding method.