Chordal Rings Based on Symmetric Odd-Radix Number Systems

摘要

An n-node network, with nodes numbered from - [n/2] to [n/2] - 1, is a chordal ring network with the chord lengths 1 = s_0, s_1, . . ., s_(k-1) (2 ≤ s_i < n/2) when each node i (- [n/2] ≤ i < [n/2]) is connected to each of the 2k nodes i ± s_i mod n (0 ≤ i < k) via an undirected link, where "mod" represents symmetric residues. We study a class of chordal ring networks in which the chord length s_i is a power of an odd "radix" r, that is, s_i = r~i, for r ≥ 3. We show that this class of chordal rings, with their nodes indexed by radix-r numbers using the symmetric digit set [- (r - 1)/2, (r - 1)/2] are easy to analyze and offer a number of advantages in terms of static network parameters and dynamic performance in many application contexts.