In this paper, a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least 6. For a J × L exponent matrix E, the lower bound Q(E) is obtained explicitly such that (J, L) QC LDPC codes with girth at least 6 exist for any circulant permutation matrix (CPM) size m ≥ Q(E). The results show that the exponent matrices constructed with ou...

For two-dimensional (2-D) digital filters implemented by a block recursive equation, explicit relations between their frequency characteristics and those of scalar filter are obtained. Specifically, these include the relation between the discrete-time Fourier transform (DTFT) of the block recursive equation and that of the scalar 2-D difference equation, and the relation between the block matri...

In this paper, five different variants of interconnection networks such as Hypercube Network, Folded Hypercube Network, Multiply Twisted Hypercube Network, Recursive Circulant Hypercube Network and Multiple Reduced Hypercube Network are illustrated using Network Simulator and various physical and logical factors such as time, size of the packet, type of packet, speed, coverage and packet loss a...

In this paper, a covariance matrix of circulant correlation, R, is studied. A pattern of entries in R−1 independent of the value ρ of the correlation coefficient is proved based on a recursive relation among the entries of R−1. The D-optimal design for simple linear regression with circulantly correlated observations on [a, b] (a < b) is obtained if even observations are taken and the correlati...

In a graph G, a k-container Ck(u, v) is a set of k disjoint paths joining u and v. A k-container Ck(u, v) is k ∗-container if every vertex of G is passed by some path in Ck(u, v). A graph G is k ∗-connected if there exists a k∗-container between any two vertices. An m-regular graph G is super-connected if G is k∗-connected for any k with 1 k m. In this paper, we prove that the recursive circula...

A 4-valent first-kind Frobenius circulant graph is a connected Cayley graph DLn(1, h) = Cay(Zn, H) on the additive group of integers modulo n, where each prime factor of n is congruent to 1 modulo 4 and H = {[1], [h],−[1], −[h]} with h a solution to the congruence equation x + 1 ≡ 0 (mod n). In [A. Thomson and S. Zhou, Frobenius circulant graphs of valency four, J. Austral. Math. Soc. 85 (2008)...

We propose a new topology for multicomputer networks, called recursive cireulant. Recursive circulant G(N, d) is defined to be a ciwulant graph with N nodes and jumps of powers of d, d 2 2. G(N,d) is node symmetric, has a hamiltonian cycle unless N 5 2, and can be recursively constructed when N = cdm, 1 5 c < d. We analyze various network metrics of G(cdm, d) such as connectivity, diameter, mea...

The matching preclusion set of a graph is a set of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The matching preclusion number is the minimum cardinality over all matching preclusion sets. We show in this paper that, for any ≥  , the matching preclusion numbers of both -dimensional restricted HL-graph and recursive circulant  ...

k-Restricted edge connectivity is an important parameter in measuring the reliability and fault tolerance of large interconnection networks. In this paper we present two families of graphs similar with the networks proposed by Chen et al. [Y.C. Chen, J.J.M. Tan, L.H. Hsu, S.S. Kao, Super-connectivity and super edge-connectivity for some interconnection networks, Applied Mathematics and Computat...

Reliability and efficiency are important criteria in the design of interconnection networks. Recently, the w-wide diameter dw(G), the (w − 1)-fault diameter Dw(G), and the w-Rabin number rw(G) have been used to measure network reliability and efficiency. In this paper, we study dw(G), Dw(G) and rw(G) using the strong w-Rabin number r∗ w(G) for 1 ≤ w ≤ k(G) and G is a circulant network G(dn; {1,...