Bounds on the Service Rates of Linear Codes and their Connections to Combinatorial Designs

Overview & Synopsis

The service rate region of a distributed storage system describes the set of concurrent demand vectors that can be served without overloading any individual server, and is a fundamental measure of how effectively redundancy is used. In this paper, we investigate aggregate service rates in distributed data storage systems based on linear codes over arbitrary finite fields. We first derive an upper bound on the aggregate service rate for an arbitrary subset of $t$ data objects in terms of the dual distance and the sizes of their smallest recovery sets. For systematic generator matrices, this bound simplifies to an expression depending only on the code length, the dual distance, and the cardinality of the selected subset. This result extends existing bounds and provides a subset-wise formulation of the First Dual Distance Bound. We then establish conditions under which this upper bound is attained. We apply our results to several important families of linear codes, including MDS codes, Reed-Muller codes, constacyclic codes, and extended Golay codes, and obtain exact values of the maximum aggregate service rates for the corresponding subsets of data objects.