AI 中文总结
本文针对高阶Reed-Muller码SRR研究的不足，通过表征恢复集交集模式推导了m=r+1时的精确区域，提供新型严格约束缩小近似与精确SRR多面体的差距，丰富了分布式存储系统并发服务能力的表征成果。
AI 中文摘要
服务率区域（SRR）是评估分布式存储系统并发服务能力的关键指标。已有研究对MDS码和一阶Reed-Muller码的SRR进行了表征，但高阶Reed-Muller码的相关问题更为复杂，Ly、Soljanin和Lalitha在[IEEE ISIT 2025]中仅给出了部分结果。本文通过明确表征高阶Reed-Muller码恢复集的交集模式，改进了SRR分析，推导了m=r+1情况下的精确区域，并提供了新型更严格的约束，以缩小现有近似与精确SRR多面体之间的差距。
英文摘要
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.
Comments6 pages, 3 figures, accepted by IEEE International Symposium on Information Theory 2026 (ISIT 2026)
