  The receiver design for multi-input multi-output (MIMO) ultra-reliable and
low-latency communication (URLLC) systems can be a tough task due to the use of
short channel codes and few pilot symbols. Consequently, error propagation can
occur in traditional turbo receivers, leading to performance degradation.
Moreover, the processing delay induced by information exchange between
different modules may also be undesirable for URLLC. To address the issues, we
advocate to perform joint channel estimation, detection, and decoding (JCDD)
for MIMO URLLC systems encoded by short low-density parity-check (LDPC) codes.
Specifically, we develop two novel JCDD problem formulations based on the
maximum a posteriori (MAP) criterion for Gaussian MIMO channels and sparse
mmWave MIMO channels, respectively, which integrate the pilots, the
bit-to-symbol mapping, the LDPC code constraints, as well as the channel
statistical information. Both the challenging large-scale non-convex problems
are then solved based on the alternating direction method of multipliers (ADMM)
algorithms, where closed-form solutions are achieved in each ADMM iteration.
Furthermore, two JCDD neural networks, called JCDDNet-G and JCDDNet-S, are
built by unfolding the derived ADMM algorithms and introducing trainable
parameters. It is interesting to find via simulations that the proposed
trainable JCDD receivers can outperform the turbo receivers with affordable
computational complexities.
