Polar codes have received a lot of attention due to their capacity-achieving performance and low complexity. This paper proposes a novel scaling offset min-sum (SOMS) algorithm and adapts the offset min-sum (OMS) algorithm for polar codes, and both algorithms are improved via learning. For all message updates, conventional min-sum decoding algorithms use the same scaling factor or offset, which is usually obtained by numerical simulations. By modeling the data flow of min-sum algorithms as a deep neural network, the parameters used in the message passing updates of min-sum decoders can be different for each message update, and are obtained by training and optimizing the corresponding deep neural network. The simulation results show that the proposed SOMS algorithm based on deep learning performs better than all existing BP-based algorithms. Moreover, this paper presents an efficient hardware architecture of the proposed SOMS algorithm. The K-Means clustering algorithm is applied to reduce the number of possible parameters of the neural network, leading to reduced energy consumption and memory requirement with negligible error performance degradation. The proposed architecture of the SOMS algorithm for a (256,128) polar code is implemented and validated on the Xilinx Artix-7 field-programmable gate array.

极地代码由于其实现容量的能力和低复杂性而受到了广泛的关注。本文提出了一种新颖的缩放最小偏移量和算法（SOMS），并将偏移最小和量算法（OMS）应用于极地码，并且两种算法都通过学习进行了改进。对于所有消息更新，常规的最小和解码算法使用相同的缩放因子或偏移量，通常通过数值模拟获得该比例因子或偏移量。通过将最小和算法的数据流建模为一个深度神经网络，最小和解码器的消息传递更新中使用的参数对于每个消息更新可以有所不同，并且可以通过训练和优化相应的深度神经网络来获得。仿真结果表明，所提出的基于深度学习的SOMS算法的性能优于所有现有的基于BP的算法。此外，本文提出了一种有效的硬件结构，提出了SOMS算法。K-Means聚类算法用于减少神经网络可能的参数数量，从而减少了能耗和内存需求，而错误性能的下降则可以忽略不计。在Xilinx Artix-7现场可编程门阵列上实现并验证了针对（256,128）极性代码的SOMS算法的建议体系结构。