一种基于错误集的极化码改进SCL译码算法

An Improved SCL Decoding Algorithm of Polar Codes Based on the Error Set

摘要:

针对极化码在中短码长时纠错性能的不足，提出了一种基于错误集的极化码改进串行抵消列表(Successive Cancellation list of Polar Codes based on Error Set, ES-SCL)译码算法。该算法首先根据极化码的信道特性构造错误集，在极化码编码时根据错误集中的元素设置奇偶校验(Parity Check, PC)位，其余位置则放置信息比特和冻结比特，译码器在译码PC位时，每条路径通过校验函数得到PC位的比特估计，不执行路径分裂和剪枝，其余位置则执行SCL译码。仿真结果表明，在加性高斯白噪声信道下，当码长为512，码率为0.5，误块率为，最大译码列表数为8时，相较于PC-PSCL译码算法以及CA-SCL译码算法，所提出的ES-SCL译码算法获得了约0.18dB和0.15dB的增益；当码长为256，码率为0.5，误码率为，最大译码列表数为8时，相较于CA-SCL，PC-PSCL译码算法，获得了约0.3dB和0.35dB的增益；此外，采用部分比特分裂译码的ES-SCL译码算法可以在误块率与PC-PSCL译码算法几乎相同的情况下，减少约50%的排序次数，具有更低的译码复杂度。

Abstract:

In order to improve the error-correction performance of polar codes with the medium and short code lengths, an improved successive cancellation list decoding algorithm based on the error set (ES-SCL decoding algorithm) of polar codes is proposed. The algorithm first constructs an error set according to the channel characteristics of polar codes. Then the parity check(PC) bits is set according to the elements in the error set during the encoding of polar codes and the information bits and frozen bits is placed in the remaining positions. When the decoder decodes the PC bits, each path don’t perform the path splitting and pruning, but can get the estimation of the PC bits through the check function. For the other bits, the decoder will directly does the SCL decoding. Simulation results show that under the additive white Gaussian noise channel, when the codes length is 512, the codes rate is 0.5, the block error rate is 10-5 and the maximum list length is 8, compared with the CA-SCL and PC-PSCL decoding algorithm, the proposed ES-SCL decoding algorithm can achieves a gain of about 0.18dB and 0.15dB .When the codes length is 256, the codes rate is 0.5, the block error rate is 10-5 and the maximum list length is 8, compared with the CA-SCL and PC-PSCL decoding algorithm, the proposed ES-SCL decoding algorithm can achieves a gain of about 0.3dB and 0.35dB. Furthermore, the ES-SCL decoding algorithm that uses the partial bit splitting decoding can reduce the sorting number of about 50% when the block error rate is almost the same as that of the PC-PSCL decoding algorithm, thus its decoding complexity is lower.