Tutorial: Statistical learning with generative models for communicati...

Learning the statistics of physical phenomena has been a long-time research objective. The advent of machine learning methods has offered effective tools to tackle such an objective in several data science domains. Some of those tools can be used in the domain of communication systems and networks. We emphasize that a distinction has to bemade among data learning and signal learning. The former paradigm is typically applied to higher protocol layers, while the latter to the physical layer. Historically, stochastic models derived from the laws of physics have been exploited to describe the physical layer. From these models, transmission technology has been developed and performance analysis carried out. Nevertheless, this approach has shown some shortcomings in complex and uncertain environments. 

Based on these preliminary considerations, in this tutorial, we will review basic concepts about the high order statistical description of random processes and conventional random signal generation methods. Then, recent generative models capable of firstlyl earning the hidden/implicit distribution and then generating synthetic signals will be discussed. We will review the concept of copula and motivate the use of recently introduced segmented neural network architectures that operate in the uniform probability space. The application of such generative models (and also of discriminative models) to classic but still open problems in communications will be illustrated, including: a) synthetic channel and noise modeling, b)coding/decoding design in unknown channels, c) channel capacity estimation.

In the above-mentioned problems, a key enabling component is the ability to estimate mutual information. This will lead us to the description of known and novel mutual information estimators. Their application will be considered to derive optimal decoding strategies with deep learning neural architectures obtained from an explainable mathematical formulation. Then, the joint design of the coding and decoding scheme aiming to achieve channel capacity will be considered. This will lead us to the discussion on autoencoders. Finally, to the most ambitious goal of estimating capacity in unknown channels. This last goal rendered possible by the exploitation of cooperative methods that learn the capacity using neural mutual information estimation.