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We propose a novel optimization-based decoding algorithm for LDPC-codedmassive MIMO channels. The proposed decoding algorithm is based on a proximalgradient method for solving an approximate maximum a posteriori (MAP) decodingproblem. The key idea is the use of a code-constraint polynomial penalizing avector far from a codeword as a regularizer in the approximate MAP objectivefunction. The code proximal operator is naturally derived from code-constraintpolynomials. The proposed algorithm, called proximal decoding, can be describedby a simple recursion consisting of the gradient descent step for a negativelog-likelihood function and the code proximal operation. Several numericalexperiments show that the proposed algorithm outperforms known massive MIMOdetection algorithms, such as an MMSE detector with belief propagationdecoding.

Proximal Decoding for LDPC-coded Massive MIMO Channels