Sphere decoder for polar codes concatenated with cyclic redundancy check

The existing cyclic redundancy check (CRC)-aided successive cancellation list (CA-SCL) decoder partitions the decoding process into two steps, where an SCL is followed by a CRC check. An SCL decoder can approach the maximum-likelihood (ML) decoding performance of the inner polar codes using a sufficiently large list; however, in this case, CRC is only used for performing error detection. Therefore, the decoding performance of the outer CRC is different from that of ML because the errors are not rectified, which degrades the performance of the entire concatenated codes. In this study, we propose a sphere decoder (SD) that can achieve the ML performance of polar codes concatenated with CRC to address the suboptimality of CA-SCL decoding. The proposed SD performs joint decoding of the CRC-polar codes in a single step, thereby avoiding the polar decoding and CRC detection decoding scheme. Because the proposed SD guarantees the ML decoding performance of the CRC-polar concatenated codes, the simulation results demonstrate that the block error rate (BLER) of the proposed SD acts as the lower bound of the CA-SCL decoding performance. Further, a new initial radius selection method is proposed for the SD to reduce the average decoding complexity. The simulations demonstrate that the proposed initial radius selection method reduces more amount of decoding complexity when compared with that reduced using sequential step size methods.