The development of power line communication (PLC) systems and algorithms is significantly challenged by the presence of unconventional noise. The analytic description of the PLC noise has always represented a formidable task and less or nothing is known about optimal channel coding/decoding schemes for systems affected by such type of noise. Recently, deep learning techniques have shown promising results and a wide range of opportunities in areas where a mathematical description of the physical phenomenon is not attainable. In this sense, the complex nature of the PLC network renders its medium characterization extremely challenging and therefore appealing for a data-driven approach. In this paper, we present a statistical learning framework to estimate the capacity of additive noise channels, for which no closed form or numerical expressions are available. In particular, we study the capacity of a PLC medium under Nakagami-m noise and determine the optimal symbol distribution that approaches it. We lastly provide insights on how to extend the framework to any real PLC system for which a noise measurement campaign has been conducted. Numerical results demonstrate the potentiality of the proposed methods.
