面向量化计算的加权图着色
Weighted Graph Coloring for Quantized Computing
AI总结：
针对两信源函数的分布式无损计算，本文提出边加权特征图及其分数着色压缩框架，刻画基本极限并实现较传统着色高逾30%的增益。
摘要：
我们考虑由一个公共用户对两个信源的函数进行分布式无损计算的问题。为此，我们首先构建一个二分图，其中两个互不相交的部分分别表示各个信源的输出结果。随后，我们将该二分图投影到每个信源上，以得到边加权特征图（EWCG），其中边权重通过信源输出结果需要被区分的程度来刻画函数结构，从而推广了特征图的经典概念。通过利用特征图、此类图的分数着色以及边权重等概念，各信源分别构建捕捉向量值信源序列的多重图，确定此类图的顶点着色，对这些着色进行编码，并将其发送给用户；用户对所接收的信息执行最小熵解码，以渐近无损的方式恢复所需函数。对于所提出的 EWCG 压缩设置，我们刻画了分布式压缩的基本极限，通过一个示例验证了通信复杂度，将其与传统着色方案进行对比，并证明相较于传统着色，我们能够获得高于 30% 的压缩增益。
英文摘要：
We consider the problem of distributed lossless computation of a function of two sources by one common user. To do so, we first build a bipartite graph, where two disjoint parts denote the individual source outcomes. We then project the bipartite graph onto each source to obtain an edge-weighted characteristic graph (EWCG), where edge weights capture the function's structure, by how much the source outcomes are to be distinguished, generalizing the classical notion of characteristic graphs. Via exploiting the notions of characteristic graphs, the fractional coloring of such graphs, and edge weights, the sources separately build multi-fold graphs that capture vector-valued source sequences, determine vertex colorings for such graphs, encode these colorings, and send them to the user that performs minimum-entropy decoding on its received information to recover the desired function in an asymptotically lossless manner. For the proposed EWCG compression setup, we characterize the fundamental limits of distributed compression, verify the communication complexity through an example, contrast it with traditional coloring schemes, and demonstrate that we can attain compression gains higher than $\% 30$ over traditional coloring.
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