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We present a novel optimization-based decoding algorithm for LDPC codes thatis suitable for hardware architectures specialized to feed-forward neuralnetworks. The algorithm is based on the projected gradient descent algorithmwith a penalty function for solving a non-convex minimization problem. Theproposed algorithm has several internal parameters such as step sizeparameters, a softness parameter, and the penalty coefficients. We use astandard tool set of deep learning, i.e., back propagation and stochasticgradient descent (SGD) type algorithms, to optimize these parameters. Severalnumerical experiments show that the proposed algorithm outperforms the beliefpropagation decoding in some cases.

Deep Learning-Aided Trainable Projected Gradient Decoding for LDPC Codes