For improving short-length codes, we demonstrate that classic decoders can also be used with real-valued, neural encoders, i.e., deep-learning based codeword sequence generators. Here, the classical decoder can be a valuable tool to gain insights into these neural codes and shed light on weaknesses. Specifically, the turbo-autoencoder is a recently developed channel coding scheme where both encoder and decoder are replaced by neural networks. We first show that the limited receptive field of convolutional neural network (CNN)-based codes enables the application of the BCJR algorithm to optimally decode them with feasible computational complexity. These maximum a posteriori (MAP) component decoders then are used to form classical (iterative) turbo decoders for parallel or serially concatenated CNN encoders, offering a close-to-maximum likelihood (ML) decoding of the learned codes. To the best of our knowledge, this is the first time that a classical decoding algorithm is applied to a non-trivial, real-valued neural code. Furthermore, as the BCJR algorithm is fully differentiable, it is possible to train, or fine-tune, the neural encoder in an end-to-end fashion.

翻译：为提升短码性能，我们证明了经典译码器可与实值神经编码器（即基于深度学习的码字序列生成器）联合使用。在此场景下，经典译码器可作为挖掘神经码深层特性并揭示其弱点的有效工具。具体而言，涡轮自编码器是一种新型信道编码方案，其编码器和译码器均由神经网络替代。我们首先证明了基于卷积神经网络（CNN）的编码因其有限感受野特性，使得BCJR算法能够以可行计算复杂度实现最优译码。这些最大后验概率（MAP）分量译码器随后被用于构建经典（迭代）涡轮译码器，以对并行或串行级联CNN编码器进行近似最大似然（ML）译码。据我们所知，这是首次将经典译码算法应用于非平凡实值神经码。此外，由于BCJR算法具有完全可微性，我们得以通过端到端方式对神经编码器进行训练或微调。