  We present a novel optimization-based decoding algorithm for LDPC codes that
is suitable for hardware architectures specialized to feed-forward neural
networks. The algorithm is based on the projected gradient descent algorithm
with a penalty function for solving a non-convex minimization problem. The
proposed algorithm has several internal parameters such as step size
parameters, a softness parameter, and the penalty coefficients. We use a
standard tool set of deep learning, i.e., back propagation and stochastic
gradient descent (SGD) type algorithms, to optimize these parameters. Several
numerical experiments show that the proposed algorithm outperforms the belief
propagation decoding in some cases.
