Collection Nexus Trimester - 2016 - Inference Problems Theme
Organisateur(s)
Date(s)
04/05/2024
The Area Theorem and Capacity-Achieving Codes – 2/2
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.
