Construction and Block Error Rate Analysis of Polar Codes Over AWGN Channel Based on Gaussian Approximation

Abstract

Polar codes are usually constructed to minimize the upper bound of a block error ratio (BLER). In this paper, we discuss the estimation of the exact BLERs of polar codes as well as the construction of polar codes. Assuming that successive cancellation (SC) decoding is employed, we present a method for estimating the exact BLER of polar codes with the help of Gaussian approximation (GA). A new algorithm is proposed to construct polar codes, aimed at minimizing the exact BLER, instead of the upper bound of the BLER. Analysis indicates that the new method is less complex than the existing methods. It is also shown that the estimation results match the simulations well.