论文标题
代码问题的服务速率的组合视图，与分数匹配的等效性以及与批处理代码的联系
A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes
论文作者
论文摘要
我们提出了一种新的技术，用于构建代码的图表表示，通过该图表，我们在服务率问题与众所周知的分数匹配问题之间建立了重要的联系。使用此连接，我们表明，编码存储系统的服务能力等于代码图表示中的分数匹配数，因此分别由匹配数和顶点盖号分别限制和上限。这引起了极大的兴趣，因为如果代码的图表示是双方的，那么派生的上限和下限是相等的，我们获得了容量。利用此结果，我们表征了二进制简称代码的服务能力，如我们所示，其图形表示为两部分。此外，我们表明服务率问题可以看作是多发射原始批次代码问题的概括。
We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we show that the service capacity of a coded storage system equals the fractional matching number in the graph representation of the code, and thus is lower bounded and upper bounded by the matching number and the vertex cover number, respectively. This is of great interest because if the graph representation of a code is bipartite, then the derived upper and lower bounds are equal, and we obtain the capacity. Leveraging this result, we characterize the service capacity of the binary simplex code whose graph representation, as we show, is bipartite. Moreover, we show that the service rate problem can be viewed as a generalization of the multiset primitive batch codes problem.
