  We propose a novel optimization-based decoding algorithm for LDPC-coded
massive MIMO channels. The proposed decoding algorithm is based on a proximal
gradient method for solving an approximate maximum a posteriori (MAP) decoding
problem. The key idea is the use of a code-constraint polynomial penalizing a
vector far from a codeword as a regularizer in the approximate MAP objective
function. The code proximal operator is naturally derived from code-constraint
polynomials. The proposed algorithm, called proximal decoding, can be described
by a simple recursion consisting of the gradient descent step for a negative
log-likelihood function and the code proximal operation. Several numerical
experiments show that the proposed algorithm outperforms known massive MIMO
detection algorithms, such as an MMSE detector with belief propagation
decoding.
