Placement Delivery Arrays from Combinations of Strong Edge Colorings

TL;DR

This paper explores methods to combine strong edge colorings of bipartite graphs to generate new placement delivery arrays (PDAs), enhancing their flexibility and potentially reducing subpacketization levels for better performance.

Contribution

It introduces novel techniques for combining strong edge colorings to create PDAs with improved parameters and robustness, expanding the design space for coded caching schemes.

Findings

Combination methods can produce PDAs with better subpacketization levels

New PDAs exhibit more flexible and robust parameters

Parameter analysis shows improvements over initial colorings

Abstract

It has recently been pointed out in both of the works [C. Shanguan, Y. Zhang, and G. Ge, {\em IEEE Trans. Inform. Theory}, 64(8):5755-5766 (2018)] and [Q. Yan, X. Tang, Q. Chen, and M. Cheng, {\em IEEE Commun. Lett.}, 22(2):236-239 (2018)] that placement delivery arrays (PDAs), as coined in [Q. Yan, M. Cheng, X. Tang, and Q. Chen, {\em IEEE Trans. Inform. Theory}, 63(9):5821-5833 (2017)], are equivalent to strong edge colorings of bipartite graphs. In this paper we consider various methods of combining two or more strong edge colorings of bipartite graphs to obtain new ones, and therefore new PDAs. Combining PDAs in certain ways also gives a framework for obtaining PDAs with more robust and flexible parameters. We investigate how the parameters of certain strong edge colorings change after being combined with others and, after comparing the parameters of the resulting PDAs with those of the initial ones, find that subpacketization levels thusly can often be improved.