论文标题
关于图表的最大存储率
On Extremal Rates of Storage over Graphs
论文作者
论文摘要
图表上的存储代码$ k $独立的源符号，$ l_w $位的每个符号，到$ n $编码的符号，$ l_v $ bits的每个符号，因此每个编码符号都存储在图的节点中，并且图的每个边缘都与一个源符号关联。从通过边缘连接的一对节点，与边缘关联的源符号可以解码。比率$ l_w/l_v $称为存储代码的符号率，最高符号率称为容量。我们表明，图表上存储代码的三个最高容量值为$ 2、3/2、4/3 $。我们表征了所有图表，其中存储代码容量为$ 2 $和$ 3/2 $，并且为$ 4/3 $的容量值，所需的条件和足够的条件（不匹配）。
A storage code over a graph maps $K$ independent source symbols, each of $L_w$ bits, to $N$ coded symbols, each of $L_v$ bits, such that each coded symbol is stored in a node of the graph and each edge of the graph is associated with one source symbol. From a pair of nodes connected by an edge, the source symbol that is associated with the edge can be decoded. The ratio $L_w/L_v$ is called the symbol rate of a storage code and the highest symbol rate is called the capacity. We show that the three highest capacity values of storage codes over graphs are $2, 3/2, 4/3$. We characterize all graphs over which the storage code capacity is $2$ and $3/2$, and for capacity value of $4/3$, necessary condition and sufficient condition (that do not match) on the graphs are given.
