Placement Delivery Array Design through Strong Edge Coloring of Bipartite Graphs

TL;DR

This paper introduces a novel interpretation of placement delivery arrays (PDAs) as strong edge colorings of bipartite graphs, enabling the construction of flexible PDAs with improved tradeoffs for coded caching.

Contribution

It establishes an equivalence between PDAs and strong edge colored bipartite graphs, allowing new PDA constructions from bipartite graph structures, including existing schemes as special cases.

Findings

PDA is equivalent to a strong edge coloring of bipartite graphs.

New PDA classes can be constructed from bipartite graph structures.

Flexible tradeoffs between sub-packetization and load are achievable.

Abstract

The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during busy times. Recently, placement delivery array (PDA) was presented to characterize both the placement and delivery phase in a single array for the centralized coded caching algorithm. In this paper, we interpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph. We prove that, a PDA is equivalent to a strong edge colored bipartite graph. Thus, we can construct a class of PDAs from existing structures in bipartite graphs. The class includes the scheme proposed by Maddah-Ali \textit{et al.} and a more general class of PDAs proposed by Shangguan \textit{et al.} as special cases. Moreover, it is capable of generating a lot of PDAs with flexible tradeoff between the sub-packet level and load.