The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with the codelength, thus they can only support short to moderate codelengths. From the point view of practicality, we propose a high-performance neural min-sum (MS) decoding method that makes full use of the lifting structure of protograph low-density parity-check (LDPC) codes. By this means, the size of the parameter array of each layer in the neural decoder only equals the number of edge-types for arbitrary codelengths. In particular, for protograph LDPC codes, the proposed neural MS decoder is constructed in a special way such that identical parameters are shared by a bundle of edges derived from the same edge-type. To reduce the complexity and overcome the vanishing gradient problem in training the proposed neural MS decoder, an iteration-by-iteration (i.e., layer-by-layer in neural networks) greedy training method is proposed. With this, the proposed neural MS decoder tends to be optimized with faster convergence, which is aligned with the early termination mechanism widely used in practice. To further enhance the generalization ability of the proposed neural MS decoder, a codelength/rate compatible training method is proposed, which randomly selects samples from a set of codes lifted from the same base code. As a theoretical performance evaluation tool, a trajectory-based extrinsic information transfer (T-EXIT) chart is developed for various decoders. Both T-EXIT and simulation results show that the optimized MS decoding can provide faster convergence and up to 1dB gain compared with the plain MS decoding and its variants with only slightly increased complexity. In addition, it can even outperform the sum-product algorithm for some short codes.

中文翻译：

---

学习解码 Protograph LDPC 码

深度学习方法的最新发展为优化线性码的置信传播 (BP) 解码提供了一种新方法。然而，现有工作的局限性在于神经网络的规模随着码长的增加而迅速增加，因此它们只能支持短到中等的码长。从实用性的角度来看，我们提出了一种高性能的神经最小和（MS）解码方法，它充分利用了原型低密度奇偶校验（LDPC）码的提升结构。通过这种方式，神经解码器中每一层的参数数组的大小仅等于任意码长的边类型数。特别是，对于原型 LDPC 码，所提出的神经 MS 解码器以一种特殊的方式构建，使得相同的参数由来自相同边缘类型的一组边缘共享。为了降低训练所提出的神经MS解码器的复杂度并克服梯度消失问题，提出了一种逐次迭代（即神经网络中的逐层）贪婪训练方法。因此，所提出的神经 MS 解码器倾向于以更快的收敛速度进行优化，这与实践中广泛使用的早期终止机制一致。为了进一步增强所提出的神经 MS 解码器的泛化能力，提出了一种码长/速率兼容的训练方法，该方法从从相同基码提升的一组代码中随机选择样本。作为理论性能评估工具，为各种解码器开发了基于轨迹的外部信息传输 (T-EXIT) 图。T-EXIT 和仿真结果都表明，与普通 MS 解码及其变体相比，优化的 MS 解码可以提供更快的收敛速度和高达 1dB 的增益，只是复杂度略有增加。此外，对于一些短代码，它甚至可以胜过 sum-product 算法。