We study the Service Rate Region of Reed-Muller codes in the context of distributed storage systems. The service rate region is a convex polytope comprising all achievable data access request rates under a given coding scheme. It represents a critical metric for evaluating system efficiency and scalability. Using the geometric properties of Reed-Muller codes, we characterize recovery sets for data objects, including their existence, uniqueness, and enumeration. This analysis reveals a connection between recovery sets and minimum-weight codewords in the dual Reed-Muller code, providing a framework for identifying those recovery sets. Leveraging these results, we derive explicit and tight bounds on the maximal achievable demand for individual data objects, thereby defining the maximal simplex within the service rate region and the smallest simplex containing it. These two provide a tight approximation of the service rate region of Reed-Muller codes.

翻译：本文研究分布式存储系统中里德-穆勒码的服务速率区域。服务速率区域是一个凸多面体，包含给定编码方案下所有可达到的数据访问请求速率，是评估系统效率与可扩展性的关键指标。利用里德-穆勒码的几何特性，我们刻画了数据对象的恢复集，包括其存在性、唯一性与枚举方法。该分析揭示了恢复集与对偶里德-穆勒码中最小权重码字之间的关联，为识别这些恢复集提供了理论框架。基于上述结果，我们推导出单个数据对象最大可达需求的显式紧界，从而定义了服务速率区域内的最大单纯形及其最小外接单纯形。二者共同构成了里德-穆勒码服务速率区域的紧致逼近。