基于CA-GA的Polar码构造算法研究

Research on Polar Code Construction Algorithm Based on CA-GA Algorithm

摘要: 针对满足低信噪比下信息可靠传输需求的问题，本文提出了一种基于优化遗传算法CA-GA的polar码构造方法。将polar码的信息子信道选择映射成N维二进制向量的优化问题，首先通过先验知识生成初始种群，再将贪婪算法引入选择过程中，然后在变异过程中引入柯西变异算子，最后根据种群适应度值自适应计算变异概率和交叉概率。进一步，以最小化误码率为目标，更新迭代生成适应度较高的种群，选取当前种群中最优秀的个体作为信息子信道索引向量，通过子信道索引向量、码长、码率以及信息位构造polar码。仿真结果表明，本文提出算法随着码长增加具有更低的误块率，在码长256、误块率为10⁻²时与GA构造法、蒙特卡洛构造法相比分别具有0.4 dB、0.5 dB的净增益，与传统遗传算法构造法相比约有0.05 dB的净增益，在码长512、误块率为10⁻²时和巴氏参数法、GA构造法、蒙特卡洛构造法相比分别具有0.5 dB、0.1 dB、0.15 dB的净增益。

Abstract: To meet the requirement of reliable information transmission under low signal-to-noise ratio, this paper proposes a polar code construction method based on an optimized genetic algorithm. The optimization problem of mapping the information sub-channel selection of polar codes into N-dimensional binary vectors involves first generating an initial population through prior knowledge, then introducing a greedy algorithm into the selection process, and finally introducing the Cauchy mutation operator in the mutation process. Finally, the mutation probability and crossover probability are adaptively calculated based on the population fitness value. Furthermore, with the goal of minimizing the bit error rate, the population with higher fitness is iteratively generated and updated. The best individual in the current population is selected as the information subchannel index vector. Using this subchannel index vector, along with the code length, code rate, and information bits, the polar code is constructed. The simulation results demonstrate that the algorithm proposed in this paper exhibits a lower block error rate as the code length increases. When the code length is 256 and the block error rate is 10⁻², it achieves a net gain of 0.4 dB and 0.5 dB compared to the Genetic Algorithm (GA) construction method and Monte Carlo construction method, respectively, and approximately 0.05 dB compared to the traditional Genetic Algorithm construction method. For a code length of 512 and a block error rate of 10⁻², it offers net gains of 0.5 dB, 0.1 dB, and 0.15 dB over the Bhattacharyya parameter method, GA construction method, and Monte Carlo construction method, respectively.