A Decoding Algorithm of Polar Codes Based on Perturbation with CNN
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摘要: 针对中短码长下串行抵消(SC)算法性能较差，且串行抵消列表(SCL)算法复杂度较高等问题，根据译码纠错空间理论，该文提出了一种基于卷积神经网络(CNN)扰动的极化码译码算法。对SC译码失败的接收序列，通过CNN产生相应的扰动噪声，并将该扰动噪声添加到接收信号中，然后根据重新计算的似然信息进行译码。仿真结果表明：与SC译码算法相比，所提出的算法约有0.6 dB的增益，与SCL(L=16)译码算法相比，该算法约有0.1 dB的提升，且平均复杂度更低。Abstract: According to the space theory for error correction, a Polar decoding algorithm for medium and short code lengths, based on the perturbation with a Convolution Neural Network (CNN), is presented to overcome the poor performance of the Successive Cancellation (SC) decoding algorithm and the high complexity of the Successive Cancellation List (SCL) decoding algorithm. For any receiving signals that failing to decode, a perturbation noise, generated through the CNN, is added to the receiving signal, and the likelihood information is then recalculated for further decoding. The simulation results show that the proposed algorithm has a gain of about 0.6 dB compared with the SC decoding algorithm, and an improvement of about 0.1 dB and a lower average complexity than that of SCL decoding algorithm when L=16.
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表 1 基于CNN扰动噪声译码算法
输入：${{y} }_1^N$, A, a, N, ite_max；
输出：$\hat u$(1) d ← SC (y) \\ SC decoding of received signal (2) if CRC (d)$ \in c$ then (3) return d as $\hat u$ (4) else (5) for i = 1 → ite_max do (6) CNN \\ Well trained CNN (7) ${n_i}$ ← CNN (y) \\ Generation of perturbation noise (8) ${y_i}$ ← y +${n_i}$ \\ Addition of perturbation noise (9) ${\rm{L}}{{\rm{R}}_i} \leftarrow {y_i}$ \\ Update LR (10) ${\hat u_i}$ ← SC $ ({\rm{LR}}_{i})$)\\ SC decoding of perturbed signal (11) if CRC (${\hat u_i} \in $) c then (12) return ${\hat u_i}$ as $\hat u$ (13) terminate Algorithm (14) else (15) Store $ {\hat u_i}$ (16) end if (17) end for (18) for i = 1 → ite_max do (19) Calculate $L({\hat u})$ from ${\hat u_i}$ (20) end for (21) max $L({\hat u})$ (22) return ${\hat u}$ as $\hat u$ (23) end if 
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表 2 CNN训练相关参数
CNN结构 {4; 18, 9, 3, 5; 128, 32, 16, 1} Mini-batch size 500 训练数据量 700000 测试数据量 200000 产生数据的SNR (dB) {0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0} 初始化方法 Xavier 优化方法 Adam
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