## 4 Results and Discussion  
To assess the proposed architecture, we employed Optiwave in tandem with MATLAB R2024a-based implementations. A concise overview of the principal simulation parameters is provided in Table 1. The system operates at a data rate of 20 Gbps and supports free-space optical (FSO) links up to a distance of 2.5 km. We adopt an LDPC code rate of 0.5 in our simulations, which provides a strong error-correction capability suitable for turbulent FSO channels. The LDPC encoder/decoder pair uses soft-decision iterative decoding (belief propagation), with a maximum of 50 iterations allowed for convergence. The atmospheric turbulence is emulated using the Gamma \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Laser power & 10 dBm \\ \hline FSO attenuation & 3 dB km\({}^{-1}\) \\ \hline Beam divergence & 2 mrad \\ \hline Transmitter aperture diameter & 5 cm \\ \hline Receiver aperture diameter & 20 cm \\ \hline Index refraction structure (\(C_{n}^{2}\)) & \(5\times 10^{-17}\text{m}^{\frac{-2}{3}}\) \\ \hline Spacing between WDM channels & 50 GHz \\ \hline Responsivity of PIN & 1 A W\({}^{-1}\) \\ \hline PIN thermal power density & \(15\times 10^{-24}\) W Hz\({}^{-1}\) \\ \hline PIN dark current & 10 nA \\ \hline Gain of electrical amplifier & 10 dB \\ \hline Electrical amplifier power spectral density & \(-60\) dBm Hz\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Gamma fading model described in Section 3, with a refractive index structure parameter C\({}_{n}^{2}\) chosen to represent strong turbulence (on the order of \(10^{-13}\) m\({}^{-2/3}\)). Unless otherwise stated, we assume a link distance L = 2 km. We also include a moderate pointing loss of 1 dB in the power budget to reflect slight alignment imperfections, and the receiver aperture diameter is set to 20 cm to capture most of the beam power (aperture averaging effect). The receiver field of view is wide enough to accommodate beam divergence over 2 km without significant clipping. Taking into account optical channel degradation and receiver noise, the parameters in Table 1 ensure a realistic evaluation of the overall performance of the system. Figure 2 illustrates the significant improvement in Bit Error Rate (BER) performance with Optical Signal-to-Noise Ratio (OSNR) when LDPC coding is applied. The dashed lines represent the original system without LDPC, where BER decreases gradually as OSNR increases but remains relatively high, especially at lower OSNR values. In contrast, the solid lines indicate the LDPC-enhanced system, which exhibits a significant reduction in BER across all measured frequencies (193.1-194.65 THz). The improvement is evident as turbulence-induced fading leads to deep signal attenuation. Without LDPC, these fades cause severe error bursts, drastically increasing BER. However, LDPC's iterative soft-decision decoding effectively reconstructs the original signal even in the presence of high bit error clusters, reducing BER by up to four orders of magnitude compared to uncoded transmission. At OSNR = 12 dB, the BER improvement is relatively modest; however, as OSNR increases, the LDPC-coded system demonstrates a steeper decline in BER, reaching values as low as \(10^{-8}\) at 32 dB OSNR, compared to \(10^{-4}\) in the original system, demonstrating its effectiveness in combating turbulence-induced signal degradation. The BER vs. OSNR results show a sizable coding gain at every frequency, with up to two orders of magnitude in BER improvement at higher OSNR levels. For instance, at 193.1 THz and an OSNR of 12 dB, the uncoded BER is around \(10^{-0.46}\), whereas the  
Figure 2: BER versus OSNR plots. LDPC-coded BER improves to \(10^{-0.76}\). As the OSNR rises to 32 dB, the uncoded BER at 193.1 THz reaches \(10^{-3.6}\), while the LDPC-coded BER pushes further to \(10^{-5.4}\).