# Two-Dimensional Permutation Vectors' (PV) Code for Optical Code Division Multiple Access Systems
## 5 Proposed 2D-PV W-T-Based OCDMA-PON  
Figure 6 shows the proposed architecture that incorporates a maximum of \(K_{1}\times K_{2}\) transmitters, \(N_{2}\) remote nodes, and \(K_{1}\times K_{2}\) receiver modules. Here, \(K_{1}\) and \(K_{2}\) represent the number of spectral and temporal code word, whereas \(N_{2}\) is the temporal code length. Each subscriber is assigned with a part of the transmitter and receiver module corresponding to a 2D vector permutation code word \(A_{g,h}\). Furthermore, a hybrid ring and tree-based topology is adapted at the feeder and distribution level to facilitate deployment of the proposed architecture as a low-cost PON. Optical source power is set to 0 decibel-milliwatts (dBm) with data bit rate 1 Giga bit per second (\(t_{b}=1\) ns). Figure 7 illustrates construction of the transmitter module in correspondence with the proposed 2D VP code word, \(A_{g,h}\). For illustration purpose, an example of a single user \(U_{0,0}\) was considered, as shown in Table 3 with a \(X^{th}\) and \(Y^{th}\) code words of \([0\;0\;1\;0\;0\;0\;1\;0]\) and \([0\;0\;1\;0\;1\;0\;0\;0]\), respectively. In addition, Table 3 shows the allocation of respective wavelengths \((\lambda_{s})\) and time delays \((\tau_{s})\) for corresponding chips in the spectral and temporal code sequences, respectively. For example, for user \(U_{0,0}\), the spectral encoding was achieved by allowing the wavelengths centered at \(\lambda_{3}\) and \(\lambda_{7}\), whereas the temporal encoding was achieved by employing \(\tau_{3}\) and \(\tau_{5}\) delay instants. Furthermore, for the user \(U_{0,0}\) under consideration, the transmitter modules incorporate a combination of broadband light sources (BBS), temporal and spectral encoders, erbium-doped fiber amplifier (EDFA), modulation, and switching arrangement. Figure 5: Receiver structure for 2D-PV OCDMA system. Figure 6: Proposed 2D PV-based OCDMA-Passive optical network architecture. Initially the broadband spectrum generated by the BBS, called light emitting diode (LED), is delivered to the temporal encoding arrangement, which contains a \(1:w_{2}\) optical splitter \((OS_{TX})\). It can be observed from Table 3 that when \(h=0\) in \(A_{g,h}\), all the \(X^{th}\) code words were delayed by the same instant. Therefore, employing a single time delay unit, in comparison with the conventional technique, can significantly reduce the complexity and cost of the system. \(OS_{TX}\) splits the incoming signal into \(w_{2}\) equal portions, which are then applied to the time delay units (TUs), as shown in Figure 6. The \(TUl_{TX}\) across each line for user \(U_{0,0}\) was proportional to the location of one chip of the time-spreading code word \(Y_{h}\), respectively, as shown in Table 3. For example, in the placement of chips in the time-spreading codeword \(Y_{1}^{T}=\{3,5\}\), suppose unit delay equals to \(\tau\), then the delay time of the \(TUl_{TX}\) for \(Y_{1}\) is \((3\tau,5\tau)\), respectively. End faces of both the \(TUl_{TX}\) were combined via \(w_{2}:1\) optical combiner (\(OC_{TX}\)) to complete the time-spreading encoding for the code words \(A_{g,0}\), respectively. Further, the output of the time-spreading encoder was delivered to an EDFA and \(1:N_{K_{1}}OS_{TX}\), where \(N_{K_{1}}\) corresponds to the number of users with reference to the spectral code words. EDFA was employed prior to the splitting arrangement in order to compensate the splitter losses and maintain the integrity of the time-spread optical pulses. For user \(U_{0,0}\), the first port of the \(1:N_{K_{1}}OS_{TX}\) was delivered to the modulating arrangement where the Mach-Zhender modulator (MZM) modulates the incoming data bits with the optical signal by using an ON-OFF keying (OOK) format. The modulated signal was delivered to the second stage of the encoding operation, namely, the spectral encoder, which was formed by the combination of \(1:w_{1}\) OS and \(w_{1}:1\) multiplexer (MUX).