A Low-complexity Decoding Algorithm Based on Parity-Check-Concatenated Polar Codes
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摘要: 极化码作为一种纠错码，具有较好的编译码性能，已成为 5G 短码控制信道的标准编码方案。但在码长较短时，其性能不够优异。作为一种新型级联极化码，奇偶校验码与极化码的级联方案提高了有限码长的性能，但是其译码算法有着较高的复杂度。该文针对这一问题，提出一种基于奇偶校验码级联极化码的串行抵消局部列表译码(PC-PSCL)算法，该算法在编码前进行外码构造，通过高斯近似(GA)得到的子信道错误概率选取较不可靠的信息位，对选取的较不可靠的信息位进行串行抵消列表(SCL)译码和奇偶校验，其余信息比特仅进行串行抵消(SC)译码。仿真结果表明，在高斯信道下，当码长为512，码率为1/2，误帧率为10–3，最大列表长度为8时，该文提出的低复杂度译码算法比SCL译码算法获得了0.5 dB的增益；与基于奇偶校验的SCL译码算法性能相近，但是空间复杂度和时间复杂度分别降低了38.09%, 15.63%。Abstract: Polar codes have perfect coding and decoding performance as a kind of error correction code, which have become a standard coding scheme for 5G short code control channel. While the length of polar codes is short, its performance is not good enough. A novel concatenating scheme, parity check codes concatenating polar codes, has improved the performance of the limited length of polar codes. However, its decoding algorithm has high complexity. In order to solve the problem, a Parity Check aided Partial Successive Cancellation List(PC-PSCL) algorithm based on parity-check-concatenated polar codes is proposed. In this algorithm, outer codes are constructed before encoding and the information bits with not enough reliability are selected through sub-channel error probability obtained by Gaussian Approximation (GA), which perform Successive Cancellation List (SCL) decoding with the help of parity check codes, while the remaining bits just perform Successive Cancellation (SC) decoding. The simulations in additive white Gaussian noise channel reveal that when the codes length is 512, the codes rate is 1/2, the frame error rate is
$ {10}^{-3} $ and the maximum list length is 8, the proposed low-complexity decoding algorithm achieves a gain of about 0.5 dB over the SCL decoding algorithm, keeps the similar performance compared with the original decoding algorithm, and the space complexity and time complexity of the decoding algorithm are reduced by 38.09% and 15.63% respectively.-
Key words:
- Polar codes /
- Parity Check (PC) code /
- Successive Cancellation List (SCL) /
- Complexity
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表 1 外码块T的取值
外码块 取值 ${{\boldsymbol{T}}_1}$ $\left\{ {56,60,62,63,64} \right\}$ ${{\boldsymbol{T}}_2}$ $\left\{ {80,88,92,93,94,95,103,104,106,107,108,109,110,111,114,115,116,117,118,119} \right\}$ ${{\boldsymbol{T}}_3}$ $\left\{ {121,144,150,151,152,154,155,156,157,158,159} \right\}$ ${{\boldsymbol{T}}_4}$ $\{ 164,166,167,168,170,171,173,178,179,181,185,196,198,$
$199,201,202,203,205,209,210,211,213,217\} $${{\boldsymbol{T}}_5}$ $\left\{ {225,226,227,229,233} \right\}$ 
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表 2 3种译码算法复杂度对比
译码算法 空间复杂度 时间复杂度 SC译码 $O(N)$ $O(N{\text{lo}}{{\text{g}}_2}N)$ PC-SCL译码 $O({L_{{\text{max}}}}N)$ $O({L_{{\text{max}}}}N{\text{lo}}{{\text{g}}_2}N)$ PC-PSCL译码 $O({L_{ {\text{max} } } }T_{i\max }^{'} + N{L_p})$ $O(({L_{{\text{max}}}}T' + {L_p}(N - T')){\text{lo}}{{\text{g}}_2}N)$
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表 3 N = 512时两种译码算法复杂度对比
译码算法 ${L_p}$ 时间复杂度 空间复杂度 PC-PSCL 1 26784 (27.34%) 1000(75.59%） 2 28224(23.44%） 1512(63.09%) 4 31104(15.63%) 2536 (38.09%) PC-SCL – 36864 4096
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表 4 N = 256时两种译码算法复杂度对比
译码算法 $ b $ 时间复杂度 空间复杂度 PC-PSCL 20% 11968(26.95%) 1136(44.53%) 30% 13024(20.51%) 1176(42.58%) 50% 13152(19.73%) 1240(39.45%) PC-SCL – 16384 2048
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