  In this paper, a deep learning (DL)-based sphere decoding algorithm is
proposed, where the radius of the decoding hypersphere is learned by a deep
neural network (DNN). The performance achieved by the proposed algorithm is
very close to the optimal maximum likelihood decoding (MLD) over a wide range
of signal-to-noise ratios (SNRs), while the computational complexity, compared
to existing sphere decoding variants, is significantly reduced. This
improvement is attributed to DNN's ability of intelligently learning the radius
of the hypersphere used in decoding. The expected complexity of the proposed
DL-based algorithm is analytically derived and compared with existing ones. It
is shown that the number of lattice points inside the decoding hypersphere
drastically reduces in the DL-based algorithm in both the average and
worst-case senses. The effectiveness of the proposed algorithm is shown through
simulation for high-dimensional multiple-input multiple-output (MIMO) systems,
using high-order modulations.
