  Following the great success of Machine Learning (ML), especially Deep Neural
Networks (DNNs), in many research domains in 2010s, several ML-based approaches
were proposed for detection in large inverse linear problems, e.g., massive
MIMO systems. The main motivation behind is that the complexity of Maximum
A-Posteriori (MAP) detection grows exponentially with system dimensions.
Instead of using DNNs, essentially being a black-box, we take a slightly
different approach and introduce a probabilistic Continuous relaxation of
disCrete variables to MAP detection. Enabling close approximation and
continuous optimization, we derive an iterative detection algorithm: Concrete
MAP Detection (CMD). Furthermore, extending CMD by the idea of deep unfolding
into CMDNet, we allow for (online) optimization of a small number of parameters
to different working points while limiting complexity. In contrast to recent
DNN-based approaches, we select the optimization criterion and output of CMDNet
based on information theory and are thus able to learn approximate
probabilities of the individual optimal detector. This is crucial for soft
decoding in today's communication systems. Numerical simulation results in MIMO
systems reveal CMDNet to feature a promising accuracy complexity trade-off
compared to State of the Art. Notably, we demonstrate CMDNet's soft outputs to
be reliable for decoders.
