论文标题
代码问题的服务速率的几何视图及其在第一阶的服务率中的应用Reed-Muller代码
A Geometric View of the Service Rates of Codes Problem and its Application to the Service Rate of the First Order Reed-Muller Codes
论文作者
论文摘要
服务速率是与分布式编码存储系统相关的最重要的，最近引入的性能指标。在其他解释中，它测量了存储系统可以同时提供的用户数量。我们引入了一种几何方法来解决此问题。这种方法比现有方法最重要的优点之一是，它允许人们在不明确知道所有可能的恢复集的列表的情况下得出代码的服务率的界限。为了说明我们的几何方法的功能，我们根据第一阶芦苇毛刺代码和单纯码的服务速率得出上限。然后，我们展示了如何实现这些上限。此外，利用所提出的几何技术，我们表明，鉴于代码的使用率区域，可以获得代码最小距离的下限。
Service rate is an important, recently introduced, performance metric associated with distributed coded storage systems. Among other interpretations, it measures the number of users that can be simultaneously served by the storage system. We introduce a geometric approach to address this problem. One of the most significant advantages of this approach over the existing approaches is that it allows one to derive bounds on the service rate of a code without explicitly knowing the list of all possible recovery sets. To illustrate the power of our geometric approach, we derive upper bounds on the service rates of the first order Reed-Muller codes and simplex codes. Then, we show how these upper bounds can be achieved. Furthermore, utilizing the proposed geometric technique, we show that given the service rate region of a code, a lower bound on the minimum distance of the code can be obtained.
