Abstract :
An optical orthogonal signature pattern code (OOSPC) finds application in transmitting 2-D images through multicore fiber in code-division multiple-access (CDMA) communication systems. Observing a one-to-one correspondence between an OOSPC and a certain combinatorial subject, called a packing design, we present a construction of optimal OOSPCs with weight 4 and maximum collision parameter 2, which generalizes a well-known Köhler construction of optimal optical orthogonal codes (OOC) with weight 4 and maximum collision parameter 2. Using this new construction enables one to obtain infinitely many optimal OOSPCs, whose existence was previously unknown. We prove that for a multiple n of 4, there exists no optimal OOSPC of size 6 n with weight 4 and maximum collision parameter 2, together with a report which shows a gap between optimal OOCs and optimal OOSPCs when 6 and n are not coprime. We also present a recursive construction of OOSPCs which are asymptotically optimal with respect to the Johnson bound. As a by-product, we obtain an asymptotically optimal (m, n, 4, 2)-OOSPC for all positive integers m and n.
Keywords :
code division multiplexing; multi-access systems; orthogonal codes; 2D images; Köhler construction; OOSPC; code-division multiple-access communication systems; maximum collision parameter 2; maximum collision weight 4; multicore fiber; optical orthogonal signature pattern codes; optimal optical orthogonal codes; packing design; Autocorrelation; Broadcasting; Multiaccess communication; Multicore processing; Optical design; Optical fiber communication; Optical fiber networks; Optical receivers; Pixel; $H$-design; Automorphism group; optical orthogonal code (OOC); optical orthogonal signature pattern code (OOSPC); packing design; space code-division multiple access;