This paper enhances the performance and training of the Turbo Autoencoder (TurboAE), an end-to-end jointly trained neural channel encoder and decoder. A novel interleaver for TurboAE with convolutional neural network (CNN) is proposed, which is shown to enhance the end-to-end performance of both TurboAE continuous and binary. Thanks to the proposed interleaver, TurboAE binary performs better than a benchmark Turbo code of length 100. In addition, a novel additional term to the loss function is proposed to improve the pairwise distance distribution of the codewords, which is shown to help the training convergence of TurboAE with CNN and recurrent neural network (RNN).

We derive iterative message passing update rules for solving the bipartite maximum weighted matching problem. It is shown that if the optimal matching solution is unique, the algorithm converges to this optimal solution at a rate comparable to the algorithm of Bayati et. al. It is shown that the two algorithms are both standard messages passing, but on dual graphs of each other. Also, the algorithm presented here requires less storage. We also provide a method to use the proposed algorithm to solve the integer maximal weighted matching problem - i.e., where the optimal solution is generally not unique