On the Service Rate Region of Reed-Muller Codes

We study the Service Rate Region (SRR) of distributed storage systems that store data using Reed-Muller (RM) codes. We focus on systems where each server stores an RM codeword symbol, and each user aims to decode a single data symbol by accessing the servers storing one of the data symbol's recovery groups. The cumulative access rate to each server cannot exceed its given service rate. The SRR is a convex polytope comprising all achievable data access request rates. It represents a critical metric for evaluating system efficiency and scalability. We characterize recovery sets for data objects using the geometric properties of RM codes. This analysis reveals a connection between the RM code's recovery sets and minimumweight codewords in the dual RM code. Using these results, we derive explicit and tight bounds for the maximal achievable demand for individual data objects, which define the maximal simplex polytope within the service rate region.