A New Polar Code Design Based on Reciprocal Channel Approximation

This paper revisits polar code design for a binary-input additive white Gaussian noise (BI-AWGN) channel when successive cancellation (SC) decoding is applied at the receiver. We focus on the so-called reciprocal channel approximation (RCA), which is often adopted in the design of low-density parity-check (LDPC) codes. Implementation of RCA requires the computation of the mutual information of BPSK signaling as well as a corresponding function known as the reciprocal channel mapping, and thus we develop rigorous closed-form approximations of these that are easy to calculate numerically and also valid over a wide range of SNR. Through numerical evaluation we find that, compared to approaches based on the popular Gaussian approximation (GA) as well as the so-called improved GA (IGA), the proposed RCA approach offers better estimates of the bit error rate of polarized channels with no additional computational cost. As a result, polar codes designed by the proposed RCA can achieve further improvement in terms of block error rate (BLER) performance. The gain achieved by the new approach becomes significant as the codeword length increases.