CRC辅助PC-polar码的新颖编码算法

针对奇偶校验极化(parity-check polar,PC-polar)码中奇偶校验码检错效率低而导致纠错性能不佳的问题，提出了一种循环冗余校验码辅助PC-polar码的新颖编码算法。用奇偶校验(PC)比特和高汉明权重的冻结比特替换低汉明权重的信息比特来优化极化码的距离谱，并结合5位循环位移寄存器优化PC码的校验函数，再在PC-polar码中加入检错效率较高的循环冗余校验(CRC)码，最后通过控制变量法确定了2种校验码的数量。仿真结果表明，该算法构造的CRC-PC-polar(CRC8,PC6)码在误块率(BLER)为10^-5时，与PC-polar码、CRC-polar码和segmented-CRC-polar码相比分别有0.4dB、0.1dB、0.2dB的净编码增益。由此可知，提出的算法能够改善PC-polar码的纠错性能。

Novel coding algorithm of the CRC-aided PC-polar codes

In order to solve the problem of the poor error-correction performance caused by the low error detection efficiency of the Parity-Check (PC) code in PC-polar codes, we propose a novel coding algorithm of the cyclic redundancy check (CRC-aided) PC-polar code. At first, the distance spectrum of the polarization codes is optimized by replacing the low hamming weight information bits with PC bits and high hamming weight frozen bits in the proposed algorithm. Second, it combines the five-bit cyclic shift register to optimize the check function of the PC code, and then the cyclic redundancy check (CRC) code with higher error detection efficiency is added into the PC-polar code. Finally, the quantity of the two check codes is determined by the control variate method. Simulation results show that compared with PC-polar code, CRC-polar code, and segmented-CRC-polar code when the block error rate (BLER) is 10^-5, the CRC-PC-polar (CRC8, PC6) code constructed by the proposed algorithm has a net coding gains of 0.4 dB, 0.1 dB and 0.2 dB respectively. As a result, the proposed algorithm can improve the error-correction performance of the PC-Polar code.