Placement Delivery Arrays from Combinations of Strong Edge Colorings

Abstract

It has recently been pointed out in both of the works [C. Shanguan, Y. Zhang, and G. Ge, IEEE Trans. Inform. Theory, 64(8):5755–5766 (2018)] and [Q. Yan, X. Tang, Q. Chen, and M. Cheng, 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, 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 edge colorings of bipartite graphs to obtain new ones, and therefore new PDA’s. We find that combining PDAs in certain ways also gives a framework for obtaining PDA’s with more robust and flexible parameters. We investigate how the parameters of certain strong edge colorings change after being combined with another, and we compare the parameters of the resulting PDA’s with those of known ones.