  Neural network decoding algorithms are recently introduced by Nachmani et al.
to decode high-density parity-check (HDPC) codes. In contrast with iterative
decoding algorithms such as sum-product or min-sum algorithms in which the
weight of each edge is set to $1$, in the neural network decoding algorithms,
the weight of every edge depends on its impact in the transmitted codeword. In
this paper, we provide a novel \emph{feed-forward neural network lattice
decoding algorithm} suitable to decode lattices constructed based on
Construction A, whose underlying codes have HDPC matrices. We first establish
the concept of feed-forward neural network for HDPC codes and improve their
decoding algorithms compared to Nachmani et al. We then apply our proposed
decoder for a Construction A lattice with HDPC underlying code, for which the
well-known iterative decoding algorithms show poor performances. The main
advantage of our proposed algorithm is that instead of assigning and training
weights for all edges, which turns out to be time-consuming especially for
high-density parity-check matrices, we concentrate on edges which are present
in most of $4$-cycles and removing them gives a girth-$6$ Tanner graph. This
approach, by slight modifications using updated LLRs instead of initial ones,
simultaneously accelerates the training process and improves the error
performance of our proposed decoding algorithm.
