A Search Algorithm to Find Multiple Sets of One Dimensional Unipolar (Optical) Orthogonal Codes with Same Code-length and Low Weight

TL;DR

This paper introduces a search algorithm for identifying multiple sets of one-dimensional unipolar optical orthogonal codes with specific parameters, auto-correlation, and cross-correlation constraints, useful in optical communication systems.

Contribution

The paper presents a novel algorithm to efficiently find multiple code sets with specified auto- and cross-correlation constraints for optical communication applications.

Findings

Successfully generated multiple code sets meeting correlation constraints

Sets can be sorted by size using Johnson bound

Applicable to optical code division multiple access systems

Abstract

This paper describes a search algorithm to find multiple sets of one dimensional unipolar (optical) orthogonal codes characterized by parameters, binary code sequence of length (n bits) and weight w (number of bit 1s in the sequence) as well as auto-correlation and cross-correlation constraint respectively for the codes within a set. For a given code length n and code weight w all possible difference sets, with auto-correlation constraints lying from 1 to w-1 can be designed with distinct code serial number. For given cross-correlation constraint from 1 to w-1 Multiple sets can be searched out of the codes with auto-correlation constraints less than or equal to given auto-correlation constraint using proposed algorithm. The searched multiple sets can be sorted as having number of codes not less than the upper bound of the sets given by Johnson bound. These one dimensional unipolar orthogonal codes have their application in incoherent optical code division multiple access systems.