Two-Dimensional Optical Orthogonal Codes and Semicyclic Group Divisible Designs
IEEE Transactions on Information Theory（2010）
摘要
A (nxm, k, ¿) two-dimensional optical orthogonal code (2-D OOC), C, is a family of nxm (0, 1)-arrays of constant weight k such that ¿i=1n¿j=0m-1A(i, j)B(i, j¿m¿) ¿ ¿ for any arrays A, B in C and any integer ¿ except when A = B and ¿ ¿ 0 (mod m ), where ¿m denotes addition modulo m. Such codes are of current practical interest as they enable optical communication at lower chip rate. To simplify practical implementation, the AM-OPPW (at most one-pulse per wavelength) restriction is often appended to a 2-D OOC. An AM-OPPW 2-D OOC is optimal if its size is the largest possible. In this paper, the notion of a perfect AM-OPPW 2-D OOC is proposed, which is an optimal (nxm, k, ¿) AM-OPPW 2-D OOC with cardinality [(m ¿ n(n-1)...(n-¿))/(k(k-1)...(k-¿))] . A link between optimal (nxm, k, ¿) AM-OPPW 2-D OOCs and block designs is developed. Some new constructions for such optimal codes are described by means of semicyclic group divisible designs. Several new infinite families of perfect (nxm, k, 1) AM-OPPW 2-D OOCs with k ¿ {2, 3, 4} are thus produced.
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关键词
mod m,group divisible design,optimal code,perfect am-oppw 2-doocis,m denotes addition modulo,two-dimensional optical orthogonal code,constant weight k,orthogonal codes,optical fibre communication,semicyclic group divisible designs,semicyclic,am-oppw 2-doocwith cardinality m,2-d,2-d ooc,2d optical orthogonal codes,current practical interest,optical communication,holey $t$ -packing,semicyclic group divisible design,am-oppw 2-d ooc,optical orthogonal code (ooc),am-oppw 2-d oocs,hamming weight,block design,chip,wireless communication,wavelength division multiplexing,binary codes
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