Distance spectrum analysis of polar codes

Abstract

The distance spectrum is used to estimate the maximum likelihood (ML) performance of block codes. A practical method which can run on a memory-constrained computer is proposed to calculate the distance spectrum of polar codes. Utilizing the distance spectrum, the frame error rate (FER) and bit error rate (BER) performances of non-systematic polar codes (NSPCs) and systematic polar codes (SPCs) are analyzed. The union bounds as well as the simulation results illustrate that, under ML decoding, SPCs are superior to NSPCs in BER performance while NSPCs and SPCs have the same FER performance.