Polar Codes with Repeating Bits and the Construction by Cluster Pairwise Error Probability

Abstract

A polar code with repeating bits (RB polar code), where a part of frozen bits only repeat their preceding information bits, is proposed. In the code construction, we propose cluster pairwise error probability (CPEP) to measure the competitiveness of the correct path against the error paths and apply CPEP as the optimization criterion for the code construction, aiming to reduce the elimination probability of the correct path in a successive cancellation list (SCL) decoder. In the simulations, the constructed RB polar codes are combined with the cyclic redundancy check (CRC) code and outperform their counterparts of CRC-concatenated polar codes over various codeword lengths, code rates, and puncturing patterns.