CAREER: Efficiency Considerations in List Decoding and Pseudorandomness Theory

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Since the pioneering work of Claude Shannon to formulate a mathematical theory of communication in 1948, the theory of error-correcting codes has enabled the practical deployment of reliable and large-scale computer and communication systems. Today, coding theory is used in virtually all aspects of computing devices: for the data exchange between different chips inside a computer, data transmission over a cable, data retention in storage devices, internet communications, household smart devices, and wireless communications in cell phones, to name a few. Modern demands for large-scale computation call for pushing the state of the art in coding techniques much further than originally envisioned by Shannon’s breakthrough, and this project aims to further that goal. The educational plans cover a broad range of contributions ranging from engagement with K-12 students, undergraduate and graduate level education, to public outreach. To pursue the broader vision of this project, the investigator focuses on the intricate connections between coding theory, particularly list decoding of error-correcting codes, and the theory of pseudorandomness at the core of computer science. Like codes, fundamental pseudorandom objects such as pseudorandom generators and randomness extractors have emerged from practical motivations, such as applications in cryptography and randomized algorithms. Furthermore, deep connections are known between these objects and error-correcting codes, particularly list decodable codes. As a result, the state of the art in both pseudorandomness and list decoding is, to a great extent, based on the same mathematical foundations. Even though the current constructions achieve remarkable guarantees in theory, they are far from the originally intended practical use. This project pursues the insight that the disconnect from practice is not merely an engineering challenge, but is mainly due to gaps in the theoretical understanding of the fundamental notions. The investigator has identified the shortcomings in theory and aims to pave the way toward optimal constructions of error-correcting codes and related pseudorandom objects that are also amenable to practical deployment. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.