Optical Orthogonal Signature Pattern Codes With Maximum Collision Parameter 2 and Weight 4

• Published in: IEEE transactions on information theory Vol. 56; no. 7; pp. 3613 - 3620
• Main Author: Sawa, Masanori
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2010; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Autocorrelation; Automorphism group; Broadcasting; Byproducts; Code Division Multiple Access; Codes; Collision parameters; Combinatorial analysis; Construction; Data transmission; H -design; Information processing; Multiaccess communication; Multicore processing; Optical design; Optical fiber communication; Optical fiber networks; optical orthogonal code (OOC); optical orthogonal signature pattern code (OOSPC); Optical receivers; Optics; Optimization; packing design; Parameter optimization; Pixel; Signatures; space code-division multiple access
• DOI: 10.1109/TIT.2010.2048487
• ISSN: 0018-9448

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.