Optimal optical orthogonal codes with new constructions for communication
On optimal (v,5,3,1) optical orthogonal codes
Information Theory
Summary
Optical orthogonal codes are special sequences used to avoid interference in optical communication systems. The authors found the best possible size for a particular type of these codes with specific parameters and call codes that reach this size optimal. They also define a perfect version of these codes that cover all difference values in a mathematical group. The paper presents ways to build infinite families of both optimal and perfect codes, advancing the design of such codes.
What this means in practice
- •For optical network engineers: Design optical communication codes that maximize data transmission while minimizing interference using the newly identified optimal code sizes.
- •For wireless system developers: Use perfect optical orthogonal codes to create sequences with ideal difference properties, improving signal clarity in spread spectrum systems.
Authors
Laura Johnson, Lorenzo Mella, Anita Pasotti, Emma Smith
Abstract
In this paper, we establish a tight upper bound for the size of a $(v,5,3,1)$ optical orthogonal code (OOC) and call such a code optimal when it achieves this upper bound. In addition, if an optimal OOC has the property that all non-identity elements of $\mathbb{Z}_v$ are covered by the list of differences of its codeword-sets then it is called perfect. In this paper, we present direct and recursive constructions for infinite classes of optimal and perfect $(v,5,3,1)$-OOCs.