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Optical orthogonal signature pattern codes (OOSPCs) play an important role in a novel type of optical code division multiple access (OCDMA) network for 2-dimensional image transmission. There is a one-to-one correspondence between an (m, n, w, λ)-OOSPC and a (λ + 1)-(mn, w, 1) packing design admitting a point-regular automorphism group isomorphic to Zm × Zn. In 2010, Sawa gave the first infinite class of (m, n, 4, 2)-OOSPCs by using S-cyclic Steiner quadruple systems. In this paper, we use various combinatorial designs such as strictly Zm × Zn-invariant s-fan designs, strictly Zm × Zn-invariant G-designs and rotational Steiner quadruple systems to present some constructions for (m, n, 4, 2)-OOSPCs. As a consequence, our new constructions yield more infinite families of optimal (m, n, 4, 2)-OOSPCs. Especially, we see that in some cases an optimal (m, n, 4, 2)-OOSPC can not achieve the Johnson bound. We also use Witt's inversive planes to obtain optimal (p, p, p + 1, 2)-OOSPCs for all primes p ≥ 3.

Variable-weight optical orthogonal code (OOC) was introduced by G-C Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this article, new infinite classes of optimal (u, W, 1, {1/2, 1/2})-OOCs are obtained for W ={3, 4}, {3, 5} and {3, 6}. q

Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.

Kitayama proposed a novel OCDMA (called spatial CDMA) for parallel transmission of 2-D images through multicore fiber. Optical orthogonal signature pattern codes (OOSPCs) play an important role in this CDMA network. Multiple-weight (MW) optical orthogonal signature pattern code (OOSPC) was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirements. Some results had been done on optimal balanced (m, n, {3, 4}, 1)-OOSPCs. In this paper, it is proved that there exist optimal balanced (2u, 16v, {4, 5}, 1)-OOSPCs for odd integers u ≥ 1, v ≥ 1.