Modern data-intensive applications, such as the Internet of Things (IoT), virtual reality, and cooperative robotics, generate large amounts of correlated data from distributed devices, making it crucial to communicate this data efficiently to optimize task performance. Two essential components in achieving this are: (1) data compression methods that effectively leverage the correlated properties of the data and are tailored to specific tasks; and (2) efficient and reliable communication algorithms designed for networked and complex communication systems. This project aims to develop innovative frameworks for constructing compression and communication algorithms to address these needs. By integrating insights from information and coding theory with modern techniques such as generative models and deep learning, the project will establish novel methodologies to drive the discovery of new algorithms. This interdisciplinary project will integrate research with several outreach and educational activities, including interactive demonstrations and educational initiatives for K-12 students, the incorporation of research findings into academic courses, engagement in research community events, collaborations with industry, and the broad dissemination of project outcomes through a tutorial blog and open-source libraries. The overarching goal of this project is to establish frameworks that integrate information theory and learning to develop new compression and communication algorithms