A practical construction method for polar codes in AWGN channels

Abstract

Polar coding, introduced by Arikan, is the first code construction method that could be proved to construct capacity-achieving codes for any symmetric binary-input discrete memoryless channels (B-DMCs). However, this construction method is not explicit or efficient if the channel is not binary erasure channel (BEC). Density evolution is proposed to help solve this problem for any B-DMCs but the implementation is not tractable and requires a high computation complexity. Here, we introduce an efficient method to calculate Bhattacharyya parameter and construct polar codes based on Gaussian approximation. Then we evaluate the code performance and compare it with the existing methods. It is shown that the constructed code using Gaussian approximation can have a comparable error performance with a low computation complexity.