Optical Orthogonal Signature Pattern Codes With Maximum Collision Parameter $2$ and Weight $4$
Optical Orthogonal Signature Pattern Codes With Maximum Collision Parameter $2$ and Weight $4$
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DOI：
10.1109/tit.2010.2048487
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发表时间：
2010-07
影响因子：
2.5
通讯作者：
M. Sawa
中科院分区：
文献类型：
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作者：
M. Sawa
在码分多址(CDMA)通信系统中，光正交签名图案码(OOSPC)被应用于通过多芯光纤传输二维图像。通过观察OOSPC与一个称为布局设计的组合问题之间的一一对应关系，提出了一种重量为4、最大碰撞参数为2的最优OOSPC的构造方法，它推广了KöHLER构造的重量为4、最大碰撞参数为2的最优光正交码。利用这种新的结构，可以得到无限多个以前未知的最优OOSPC。证明了对于n的4的倍数，不存在权值为4、最大碰撞参数为2、大小为6n的最优OOSPC，并证明了当6和n不互质时，最优OOSPC与最优OOSPC之间存在差距。我们还给出了OOSPC的递归构造，这些OOSPC关于Johnson界是渐近最优的。作为副产品，我们得到了所有正整数m和n的渐近最优的(m，n，4，2)-OOSPC。
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.