Combinatorial constructions for optimal multiple-weight optical orthogonal signature pattern codes

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• 作者：Hengming Zhao ; ^{hengmingzh@163.com" class="auth_mail" title="E-mail the corresponding author} ; Rongcun Qin ^{qinrongcun@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Optical orthogonal signature pattern code ; Difference packing ; Relative difference family ; Incomplete difference matrix
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 January 2016
• 年：2016
• 卷：339
• 期：1
• 页码：179-193
• 全文大小：449 K

文摘

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) requirement. In this paper, an upper bound on the maximum code size of (u&times;v,W,1,Q)$(u\&<font\; color="red">time</font>s;v,W,1,Q)$-OOSPC is improved. By using quadratic residues and skew starters, some direct constructions for balanced (3&times;gv,3&times;g,{3,4},1)$(3\&<font\; color="red">time</font>s;gv,3\&<font\; color="red">time</font>s;g,\{3,4\},1)$-OOSPCs are given for some positive integers g$g$ and v$v$. Several recursive constructions for balanced (u&times;v,W,1)$(u\&<font\; color="red">time</font>s;v,W,1)$-OOSPCs are presented by means of incomplete difference matrices and perfect relative difference families. By using those constructions, a balanced optimal (3u&times;9v,{3,4},1)$(3u\&<font\; color="red">time</font>s;9v,\{3,4\},1)$-OOSPC is obtained for any pair of positive integers (u,v)$(u,v)$ with gcd(u,3)=1$gcd(u,3)=1$.