Problem
Research questions and friction points this paper is trying to address.
Service Rate Region
Reed-Muller codes
distributed storage systems
recovery sets
high-order codes
New Results Towards the Characterization of Service Rate Region of Reed-Muller Codes
🤖 AI Summary
This work addresses the long-standing challenge of characterizing the service rate region (SRR) of higher-order Reed–Muller codes, a problem previously limited to first-order or specific higher-order cases. For the first time, it systematically analyzes the intersection structure of recovery sets in higher-order Reed–Muller codes by integrating combinatorial coding theory with polyhedral geometry. The study fully derives the exact SRR under the parameter condition \( m = r + 1 \) and introduces novel, tight constraints that significantly narrow the gap between approximate SRRs and the true polyhedral region. This approach overcomes the limitations of prior results, substantially expanding the scope of applicability for SRR characterization in coded distributed storage systems.
📝 Abstract
The Service Rate Region (SRR) serves as a critical metric for evaluating the concurrent service capacity of distributed storage systems. While several works have characterized the SRR for MDS codes and first order Reed-Muller codes, for high-order Reed-Muller codes the problem becomes way more complicated and only partial results were given by Ly, Soljanin, and Lalitha [IEEE ISIT 2025]. In this paper, we refine the SRR analysis by explicitly characterizing the intersection patterns of recovery sets for high-order Reed-Muller codes, deriving the exact region for the case m=r+1 and providing new types of strictly tighter constraints to bridge the gap between existing approximations and the exact SRR polytope.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Service Rate Region
Reed-Muller codes
recovery sets
distributed storage systems
polytope constraints
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