Collaborative Research: CIF: Small: Designing Plotkin Transform Codes via Machine Learning

Reliable communication, enabled by codes, is a primary workhorse of the information age. Successful code design (e.g., convolutional codes, Turbo codes, low-density parity-check codes, and polar codes ) is sporadic and largely a product of individual human ingenuity, although the impact on humanity is enormous -- every cellphone designed uses one of these codes. In this project, we bring the tools of machine learning (ML) and deep learning (DL) to better decode existing codes and invent new code families, speeding up the code design process. The project also includes open-source code releases, graduate student mentoring, and outreach efforts to broaden participation in the field. This project investigates a family of codes called Plotkin Transform (PT) codes, which include Reed-Muller and polar codes as special cases (both are capacity achieving and polar codes are used in the 5G global cellular standard). Although Reed-Muller codes and polar codes were invented entirely independently (and six decades apart in time), PT codes provide a common framework design via the computation tree of the Kronecker Operation central to Reed-Muller and polar codes. This project exploits the PT code framework to explore the underlying design structures that enable good encoding and decoding properties via the tools of ML and DL to systematically generalize the family of PT codes by nonlinear parameterizations; data-driven methods allow us to explore the space of parameters via optimization techniques, such as gradient descent. The overall goal is to invent new codes within the generalized nonlinear PT code family as well as new decoder algorithms for both the standardized Reed-Muller and polar codes. 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.