Near Maximum Likelihood Decoding with Deep Learning.

A novel and efficient neural decoderalgorithm is proposed. The proposed decoderis based on the neural Belief Propagationalgorithm and the AutomorphismGroup. By combining neural belief propagationwith permutations from the AutomorphismGroup we achieve near maximum likelihood performance for High Density Parity Check codes. Moreover, the proposed decodersignificantly improves the decodingcomplexity, compared to our earlier work on the topic. We also investigate the training process and show how it can be accelerated. Simulations of the hessian and the condition numbershow why the learning process is accelerated. We demonstrate the decodingalgorithm for various linear block codesof length up to 63 bits.