Interleaving Schemes on Circulant Graphs

Interleaving schemes are used for error-correcting on a noisy channel. We consider interleaving schemes on infinite circulant graphs with two offsets 1 and d, with a goal to minimize the interleaving degree. Our constructions are minimal covers of the graph by copies of some subgraph S that can be labeled by a single label. We focus on minimizing the index of S - an inverse of its density rounded up. We establish lower bounds and prove that our constructions are optimal or almost optimal, both for the index of S and for the interleaving degree. We identify related combinatorial questions and advance conjectures.