CRC-Aided Sphere Decoding for Short Polar Codes

Abstract

Polar codes have recently been adopted as a coding scheme for fifth-generation wireless systems, owing to their excellent performance at short code lengths. In this letter, we propose a cyclic redundancy check (CRC)-aided sphere decoding (CA-SD) algorithm to further improve the performance of short polar codes. It provides better performance than the widely used CRC-aided successive cancellation list (CA-SCL) decoding, and it is robust to the CRC length that leads to the stable performance under a wide range of code rates. By employing the Gaussian elimination method, we transform the underlying parity check relationships in CRC as the equivalent new forms. This ensures the parity check bits can be uniquely judged by previous decoded bits rather than the redundant search during the CA-SD. By this means, the complexity of CA-SD is reduced and comparable with the CA-SCL decoding under short code lengths.