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

通过代码实现的可靠通信是信息时代的主要工作。成功的代码设计（如卷积码、Turbo码、低密度奇偶校验码和极性码）是零星的，很大程度上是人类个人聪明才智的产物，尽管它们对人类的影响是巨大的——每一款设计出来的手机都使用了其中一种代码。在这个项目中，我们带来了机器学习（ML）和深度学习（DL）的工具，以更好地解码现有代码并发明新的代码族，加快代码设计过程。该项目还包括开源代码发布、研究生指导以及扩大该领域参与的推广工作。该项目研究了一组称为Plotkin Transform （PT）的代码，其中包括Reed-Muller代码和极性代码作为特殊情况（两者都是容量实现和极性代码在5G全球蜂窝标准中使用）。虽然Reed-Muller码和极性码是完全独立发明的（并且相隔60年），但PT码通过Kronecker操作的计算树为Reed-Muller码和极性码提供了一个通用的框架设计。该项目利用PT代码框架探索底层设计结构，通过ML和DL工具实现良好的编码和解码特性，通过非线性参数化系统地推广PT代码族；数据驱动的方法允许我们通过优化技术（如梯度下降）来探索参数空间。总体目标是在广义非线性PT码族中发明新的代码，以及标准化Reed-Muller和polar码的新解码器算法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.