Powerline communication and the 36 officers problem

In this survey paper, we explore the interactions between mathematics and engineering inspired by the challenge of transmitting data along powerlines. In particular, we focus on how combinatorial objects called permutation arrays offer a way of encoding data which allows the noise problems experienced in powerline communications (PLCs) to be overcome. The first study of permutation codes was carried out in the 1970s, but the preference in traditional information theory for codes with small alphabet size meant that permutation codes were largely ignored until recently. Their rediscovery for use in PLCs has brought about a resurgence of interest in the construction and properties of permutation arrays. We survey previous and current work in this area, and discuss future developments.