Maximal Coding Rate Reduction: A Unified Approach for Task-Oriented RIS and Communication

Reconfigurable intelligent surfaces (RIS) have shown promise in enhancing wireless communication by intelligently adjusting signal propagation. This study explores a RIS-assisted multi-device communication system focusing on task-oriented communication in edge server inference tasks. Unlike traditional RIS designs that optimize channels without task relevance, we propose a unified objective, maximal coding rate reduction (MCR<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula>), to optimize RIS, feature encoder, and channel precoder. We introduce alternative block gradient projection (ABGP) and reflecting gradient project (RGP) algorithms to design precoder and RIS. Simulation results demonstrate that our approach significantly outperforms conventional methods in extreme indoor environments with low signal-to-noise ratio (SNR). It achieves comparable performance to general RIS designs with fewer elements, ensuring task-specific enhancements. We further extend our method to active RIS, addressing the double path fading issue in passive RIS and improving performance under equal power budgets.