A New Perspective on Polar Codes: Analysis of Bit Error Probability
Bolin Wu, Kai Niu, Jincheng Dai · IEEE Transactions on Communications · 2024
This paper conducts the first analysis of the bit error probabilityPbof polar codes under successive cancellation (SC) decoding, with a focus on information bits. We introduce the concept of component bit error probabilityPb(i), which corresponds to thei-th stage of SC decoding, andPbis computed as the sum of allPb(i) over the information set. To facilitate the evaluation ofPb(i) andPb, we propose an analytical approach that leverages the algebraic structure of a particular type of polar codes termed polar subcodes. This approach allows us to derive closed-form approximations for the upper bounds on bothPb(i) andPb. Our analysis applies to both systematic and non-systematic polar codes, where we further investigate the homogeneity and introduce the input-output weight distribution of polar subcodes to obtain more concise expressions for the proposed approximate upper bounds. Experimental results are also presented to validate the effectiveness of these approximations.