Appears in collection : 2016 - T1 - WS4 - Inference problems theme

The area theorem can be thought of as a conservation law for error correcting codes. It is a mathematical formulation of the fact that there are no “good” or “bad” codes, only codes of different characteristic. I will start from scratch and first show the very simple derivation of the area theorem and then discuss its consequences. In particular I will discuss what it tells us about capacity-achieving codes. In particular I will review a recent result by Kudekar, Kumar, Mondelli, Pfister, Sasoglu and Urbanke that shows that Reed-Muller codes achieve capacity on the binary erasure channel where the area theorem plays a crucial role.