This paper proposes a node-classified redundant decoding (NC-RD) algorithm based on the received sequence's channel reliability for high-density parity-check (HDPC) codes. Two preprocessing steps are proposed prior decoding. The variable nodes of the parity-check matrix are firstly classified by the k -median algorithm based on the number of shortest cycles associated with each variable node before decoding. Then, by searching among the automorphism group of the HDPC codes, we generate a list of permutations for bit positions by computing and sorting the permutation reliability metrics. The redundant decoder conducts the message-passing decoding according to the sorted permutations, which limit the unreliable information propagation for each permutation. Besides proposing a list decoding algorithm on top of the NC-RD algorithm to augment the decoder's performance, we show that the NC-RD algorithm can be transformed into a neural network system. More specifically, multiplicative tuneable weights are attached to the decoding messages to optimize the decoding performance. Simulation results of BCH codes over the AWGN channels show that the NC-RD algorithm provides a performance gain compared to the random redundant decoding algorithm. Additional decoding performance gain can be obtained by both the list decoding method and the neural network “learned” NC-RD algorithm.

中文翻译：

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一种深度学习辅助的BCH码节点分类冗余解码算法


本文提出了一种基于接收序列信道可靠性的高密度奇偶校验（HDPC）码的节点分类冗余解码（NC-RD）算法。在解码之前提出了两个预处理步骤。在解码之前，奇偶校验矩阵的变量节点首先根据与每个变量节点相关联的最短周期的数量通过k中值算法进行分类。然后，通过在 HDPC 码的自同构群中进行搜索，通过计算和排序排列可靠性度量来生成比特位置的排列列表。冗余解码器根据排序后的排列进行消息传递解码，限制了每个排列的不可靠信息传播。除了在 NC-RD 算法之上提出一种列表解码算法来增强解码器的性能之外，我们还表明 NC-RD 算法可以转化为神经网络系统。更具体地，乘法可调权重被附加到解码消息以优化解码性能。 BCH 码在 AWGN 信道上的仿真结果表明，与随机冗余解码算法相比，NC-RD 算法提供了性能增益。列表解码方法和神经网络“学习”NC-RD 算法都可以获得额外的解码性能增益。