A signal-alignment theory in rolling-based lightwave transmission systems

A theory to support signal alignment in rolling-based lightwave transmission systems is developed. The theory originates from the transmission system environment, which consists of three basic building blocks-multiplexer, scrambler, and permuter. These building blocks are represented by mathematical operators, on the basis of which mathematical expressions of the whole transmission system become possible. The mathematical operators are directly translated into number operators which help detect and identify the received signals in the form of a table-the signal-detection table. The signal-detection tables play a central role in the signal-alignment theory, since any transmission system can be represented by its corresponding signal-detection table. The entries in the signal-detection tables are closely correlated so that the tables can be uniquely characterized by their corresponding characteristic expressions. Various types of signal-detection tables are examined, and solutions to align transmitted signals and to reduce signal-alignment time in rolling-based lightwave transmission systems are exemplified through scrambler-permuter configurations