This paper studies two crucial problems in the context of coded distributed storage systems directly related to their performance: 1) for a fixed alphabet size, determine the minimum number of servers the system must have for its service rate region to contain a prescribed set of points; 2) for a given number of servers, determine the minimum alphabet size for which the service rate region of the system contains a prescribed set of points. The paper establishes rigorous upper and lower bounds, as well as code constructions based on techniques from coding theory, optimization, and projective geometry.

翻译：本文研究编码分布式存储系统中与其性能直接相关的两个关键问题：1）对于固定的字母表大小，确定系统必须具有的最小服务器数量，以使其服务速率区域包含指定的点集；2）对于给定的服务器数量，确定系统服务速率区域包含指定点集所需的最小字母表大小。本文基于编码理论、优化和射影几何的技术，建立了严格的上界和下界，并提出了相应的编码构造方法。