Multi-CRC Polar Codes and M-SCFlip-Based Decoding

Abstract

A multi-cyclic redundancy check (Multi-CRC) polar code construction algorithm is proposed in this paper to solve the error propagation problem of successive cancellation decoding for polar codes. In this algorithm, the information sequence is optimized into several segments to allow decoding errors to be corrected in time, minimizing the impact of error propagation. An improved multi-successive cancellation bit flipping (M-SCFlip) decoding algorithm is proposed to execute the bit flipping operation after CRC check-in each segment. In the low-SNR region, the proposed new multi-CRC polar code with successive cancellation list (SCL) decoding has a slight frame-error rate (FER) degradation compared with the original CRC polar code. With the M-SCFlip decoding algorithm developed in this paper, it achieves a better FER performance compared with the CRC polar code with successive cancellation (SC) and SCL (L =2) decoding algorithms. In addition, it has a lower decoding delay and requires a lower memory space. For example, at a FER of 10-4 with the same code length and effective code rate, the proposed multi-CRC polar code with M-CFlip decoding achieves a 1.19 dB and 0.79 dB gains over existing CRC polar codes with the SC and SCL (L =2) decoding algorithms, respectively.

Keywords

• Polar codes
• successive cancellation decoding
• error propagation
• multi-bit flipping