## 3 System Architecture  
The proposed WDM-PON-FSO system is designed to provide seamless high-speed connectivity. The system architecture shown in Figure 1 consists of a centralized baseband unit (BBU), an optical line terminal (OLT), multiple optical network units (ONUs), an LDPC encoder and decoder, and a free-space optical (FSO) link that extends connectivity to remote locations. The centralized baseband unit (BBU) serves as the primary control node, managing both data transmission and reception tasks within the network. To facilitate WDM-PON operations and make efficient use of available bandwidth, it employs a multi-wavelength comb source that generates multiple optical carriers. Moreover, it utilizes digital signal processing (DSP) techniques, most notably LDPC coding and decoding, to minimize errors and maintain high-quality signal performance. Positioned at the interface with the core network, the Optical Line Terminal (OLT) directs optical signals toward Optical Network Units (ONUs) through a WDM-PON infrastructure. It relies on arrayed waveguide gratings (AWGs) to handle multiplexing and demultiplexing processes, ensuring precise separation of individual channels. At each subscriber location, an Optical Network Unit (ONU) is responsible for extracting data transmitted by the WDM-PON-FSO configuration. These ONUs also include LDPC-based error correction modules, which improve signal fidelity prior to further data processing. Optical link turbulence, whether moderate or severe, can be quantified via the Rytov variance. Concurrently, scintillation induces fluctuations in signal intensity, ultimately undermining system performance. To mitigate these effects, advanced Low-Density Parity-Check (LDPC) codes are employed, thereby enhancing the system's resilience in the face of noise and atmospheric perturbations. The LDPC encoder adds redundancy during transmission by using a generator matrix to convert a binary input sequence of length \(k\) into a binary output sequence of length \(n\). The first \(n-k\) bits in the output represent parity information derived from the encoding procedure, while the remaining \(k\) bits map directly to the original input sequence. A sparse parity-check matrix \(H\), comprising \(n-k\) rows and \(n\) columns, underpins effective error correction by satisfying the condition:  
\[H\cdot c^{T}=0,\]  
where \(c\) denotes the encoded codeword vector. At the receiver, the LDPC decoder employs the belief propagation (sum-product) algorithm to iteratively recover the transmitted data from the received noisy version. The decoder uses soft-decision decoding to estimate the original binary sequence and applies the log-likelihood ratio (LLR) calculation:  
\[\text{LLR}(y_{i})=\log\left[\frac{P(y_{i}\mid c_{i}=0)}{P(y_{i}\mid c_{i}=1)} \right],\]  
Figure 1: The WDM FSO architecture. where \(P(y_{i}\mid c_{i})\) represents the conditional probability of receiving \(y_{i}\) given that the transmitted bit was \(c_{i}\). The decoding process iteratively updates probability estimates, ensuring minimal latency while maintaining high accuracy. The proposed architecture combines a WDM-PON backbone with a free-space optical (FSO) link, using LDPC coding and OFDM modulation to ensure high reliability. On the transmitter side, a central baseband unit (BBU) hosts a multi-wavelength source (such as a comb laser) feeding an arrayed waveguide grating (AWG) for WDM multiplexing of numerous 1550 nm-band channels. Each optical carrier is intensity-modulated with a high-speed OFDM signal carrying the data. The data stream first passes through an LDPC encoder, which adds redundant parity bits for error correction. Next, the encoded bits are mapped to QAM symbols (16-QAM in this design) and distributed across many subcarriers by an OFDM modulator. Each WDM channel uses a non-return-to-zero (NRZ) pseudo-random bit sequence (PRBS) of length \(2^{23}-1\) at a data rate of 40 Gbps. In the OFDM modulator, 512 subcarriers are used along with a 2048-point Fast Fourier Transform (FFT).