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.

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