# Optical Code Construction of 2D Spectral/Spatial BIBD Codes for SAC-OCDMA Systems
## 1 Introduction  
The main parameters used to measure performance of Optical code division multiple access (OCDMA) system are available bandwidth, signal-to-noise ratio (SNR), and the cross-correlation between coded signature sequences [1]. Major development in the optical access technology can assure increased bandwidth and improved data rates with higher numbers of supported users [2]. In OCDMA, a number of coding methods are available-frequency hopping [3, 4], time spreading [5, 6, 7], spectral polarization [8], spatial and spectral amplitude coding (SAC) [8]. In all of these, SAC has gotten more attention in recent years as codes with fixed in phase cross-correlation (IPCCs) and zero cross-correlation (ZCC) properties are used. Such codes with efficient detection schemes can effectively suppress the multiple user interference (MUI) among codes [9]. Wavelengths based on user data can be chosen using low cost fiber Bragg grating (FBG) filters for encoding purposes in case of SAC based OCDMA system. Additionally, incoherent optical sources such as white light LEDs make its implementation low-cost when compared to existing data encoding techniques [10]. However, 1D codes used inSAC systems have some drawbacks such as large code length resulting in complex code construction and restrained code cardinality and bandwidth. This limits its scope only for short distance communication, specifically for fiber to the home (FTTH) and local area network (LAN) applications [11; 12]. [PERSON] and [PERSON] [13] presented 2D optical orthogonal codes (OOC), with increased cardinality and good auto and cross-correlation properties for OCDMA systems. In particular, 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) are the coding dimensions in OCDMA schemes [14]. 1D codes are bandwidth inefficient due to their large code length because they are governed by optical broadband source (BBS) which also limits the number of supported users [15]. The code length is inversely proportional to the number of users, therefore, fewer users can be accommodated. In addition, to efficiently encode the optical spectrum, noncoherent optical sources with relatively high chip width and FBGs are used resulting in a large bandwidth. Conventional SAC-OCDMA systems using 1D codes limit the suppression of intensity noise (IN). Therefore, a coding scheme with optimal length and ideal cross correlation code properties is desirable because it can provide enhanced system capacity in terms of data rate and code cardinality. For these reasons, 2D codes have been proposed and designed by combining two different dimensions of CDMA. 2D codes with dimensions (spectral/time, spectral/spatial, and time/spatial) lead to efficient bandwidth utilization with better performance in terms of increased users due to spectral density expansion at the cost of high-speed electronic devices [16]. Moreover, 2D coding techniques, especially based on wavelength/time (W/T) and spectral/spatial S/S, result in higher transmission capability and more flexibility as compared to 1D and 2D time/spatial (T/S) coding approaches [17]. Further, reported 2D codes can be divided into two types: conversion of 1D sequences to 2D codes [17] and hybrid sequences in which one type of code sequence is crossed with another in order to increase the cardinality as well as to improve correlation properties [18; 19]. Thus, as a trade-off among different performance characteristics, different coding approaches being studied can be used for specific applications. [PERSON] et al. [18] presented construction of 2D W/T hybrid code (optical complementary code and balanced incomplete block design (BIBD) zero cross-correlation codes) which is constructed using BIBD design. The proposed code showed ZCC properties and results indicated an increase in the number of supported users. For SAC based OCDMA systems, novel 2D hybrid code is introduced, and performance is compared with existing 2D M-matrices code in [19].