The Power of Symmetry in Coding and Sensing

Over the past decade, researchers have made significant progress in understanding when structured systems for data recovery achieve their theoretical limits. For error-correcting codes, which enable reliable communication despite data loss or noise, some symmetric code families (such as Reed-Muller and BCH codes) are now known to achieve optimal throughput on erasure channels. Compressed sensing, where the goal is to reconstruct a high-dimensional sparse signal from a small number of linear measurements, is known to have a strong mathematical connection to error-correcting codes. In this talk, I will explore how symmetry can provide strong performance guarantees for both problems. All results will be introduced using linear algebra and probability without assuming knowledge of coding theory or compressed sensing.