An Optimized Method for Polar Code Construction

Abstract

Polar codes are traditionally constructed by calculating the reliability of channels, then sorting them by intensive calculations to select the most reliable channels. However, these operations can be complicated especially when, the polar code length, N becomes great. This paper proposes a new low-complexity procedure for polar codes construction over binary erasure and additive white Gaussian noise (AWGN) channels. Using the proposed algorithm, the code construction complexity is reduced from O(Nlog N) to O(N), where N=2n (n≥1). The proposed approach involves storing the classification of channels by reliabilities in a vector of length L, and then deriving the classification of M channels for every M where M<=L. The proposed method is consistent with Bhattacharya parameter based Construction and Density Evolution with Gaussian Approximation (DEGA) based construction. In this paper, the Successive Cancellation Decoding algorithm (SCDA) is used. Thanks to its low complexity and its high error-correction capability.