Applications and Constructions of Optical Codes With Large Cardinality and Multiple Tree Structures

Algebraic optical codes with large cardinality and unique tree structures of multiple levels of subsets of codewords for adjustable code performance and cardinality have recently been proposed. As shown in this paper, these characteristics support new network architecture and applications for rapid code switching and physical-layer security in optical code-division multiple access networks. In addition, a new “translate” method of converting “additive” error-correction codes (ECCs) into this kind of optical codes is investigated and demonstrated with four families of Reed-Solomon codes. With rich families of ECCs, our method enhances the collections of optical codes. The performances of these “tree-structured” optical codes are algebraically analyzed and verified, for the first time, using the weight distribution of ECCs.