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，我们证明经典译码器也可与实值神经编码器（即基于深度学习的码字序列生成器）协同工作。在此框架下，经典译码器可作为探究神经编码特性、揭示其缺陷的有效工具。具体而言，涡轮自编码器是一种新型信道编码方案，其编码器与译码器均由神经网络替代。我们首先证明，基于卷积神经网络（CNN）的编码器受限感受野特性，使得BCJR算法能以可行计算复杂度实现最优译码。这些最大后验概率（MAP）分量译码器进而可构建用于并行或串行级联CNN编码器的经典（迭代）涡轮译码器，从而实现对学习编码的准最大似然（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编码。此外，由于BCJR算法具有完全可微性，因此可通过端到端方式训练或微调神经编码器。