# A New Hybrid Prime Code for OCDMA Network Multimedia Applications
## 1 Introduction  
In the last three decades, there were two main categories of optical orthogonal codes, based on (0, 1) logic, and were introduced into the optical code division multiple access (OCDMA) networks. The first code category refers to the optical orthogonal codes (OOCs) and is designed with low off-peak, auto- and cross-correlation properties for the purposes of frame synchronization and minimum interference [1, 2, 3, 4, 5, 6, 7, 8, 9]. The second one refers to the prime codes (PCs) and is designed to sacrifice the auto-correlation property [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. In direct sequence OCDMA (DS-OCDMA) networks, each user assigns a different code sequence to spread its data bits. Moreover, all code sequences are orthogonal and share the same available bandwidth such as the OOCs, MPCs, and other spreading codes in the literatures. Before the spreading, line coding such as block codes can be used at the bit level in order to detect and correct the data bits at the receiving end.  
In order to improve the OCDMA network's performance, many researchers have focused on the modification of the OOC and PC parameters such as code length, code weight, and code correlation properties. Ultimately, the total number of code sequences provided is the most important network parameter. It limits the number of users sharing the network simultaneously. To date, all of the previous results demonstrated that the PC family such as; modified PCs (MPCs), padded MPCs (PMPC), new-MPCs (n-MPC), doublepadded MPCs (DPMPCs), uniform cross-correlation MPCs (UC-MPCs), enhanced MPCs (EMPCs), and weighted MPCs (WMPCs) can offer a greater number of sequences with much better characteristics than the OOC [22; 23; 24; 25; 26].  
Within the PC family, the WMPC is an improvement over MPC, i.e., double the number of code sequences, higher code weight, and better correlation properties assuming the same PC sequence length [27; 28; 29; 30; 31; 32; 33]. The MPC uses complex analysis methods to increase the code weight to further comply with the auto-correlation peak value. From these observations, the main objective of this study is to propose a new code family called hybrid prime codes (HPC) that is not related to the MPC and their method of construction but only depends on the code words of the PC. This new code family is able to provide data for the following issues efficiently:  
1. Maximum number of code sequences for maximum number of users, leading to an increase in the network capacity for data and multimedia applications.
2. Minimum code length to increase the user bit rate.
3. Optimal code weight for good network bit error rate (BER) performance.
4. Minimum cross-correlation values to prevent multiple access interference (MAI).
5. Reliable code parameter variation while keeping the same cross-correlation value.
6. Simplicity of code generation.
7. Minimum cost with respect to the line coding techniques in optical domain.  
Two main goals required for a high performance OCDMA network:  
1. High signal integrity in the midst of interference at the receiving end.
2. Broader network capacity.  
Therefore, all optical code sequences have to be in the optical orthogonal category in order to distinguish the target user from the rest.  
The remainder of this paper is organized as follows. Section 2 is a literature review on the 2-D OCDMA codes. The construction principles and correlation properties of the HPC are introduced in Section 3. Section 4 shows the code correlation results. The proposed OCDMA system model is illustrated in Section 5. Section 6 is the BER performance analysis, while Section 7 is the throughput analysis. Section 8 displays and discusses the simulation results. Section 10 is devoted to the main conclusions.