从组合论的角度看码的服务率问题与分数匹配的等价性及其与批码的联系
A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes
摘要：
我们提出了一种新的技术，用于构建一个图形表示的代码，通过它，我们建立了一个显着的服务率问题和著名的分数匹配问题之间的连接。使用这种连接，我们表明，编码存储系统的服务容量等于分数匹配数的图形表示的代码，因此是下界和上界的匹配数和顶点覆盖数，分别。这是非常有趣的，因为如果代码的图形表示是二分的，那么导出的上界和下界是相等的，并且我们获得了容量。利用这一结果，我们的特点的二进制单工码的图形表示，如我们所示，是二分的服务能力。此外，我们表明，服务率问题可以被看作是一个推广的多集原始批码问题。
英文摘要：
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.
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