# Bandwidth Density Analysis of Coded Free-Space Optical Interconnects
###### Abstract
Noise can degrade the performance of FSOIs systems and limit their data transmission capabilities [15]. Two primary sources of noise impact FSOI channels: channel-to-channel crosstalk and thermal noise associated with the detector amplifier. Channel-to-channel crosstalk occurs when there is an overlapping or interference of signals between adjacent channels in FSOIs systems. This phenomenon is primarily caused by light diffraction, which leads to signal leakage and interference among neighboring links. Crosstalk noise can result in a decrease in signal quality, increased bit errors, and a reduction in the achievable data rate. Managing and mitigating channel-to-channel crosstalk is crucial for ensuring reliable and high-performance FSOI communication. Thermal noise is another significant source of noise in FSOI channels and is associated with the presence of detector amplifiers. Thermal noise occurs due to the random thermal energy present in the system that leads to fluctuations in the electrical signal generated by the detector. This noise contributes to the overall noise floor of FSOI systems. Therefore, it limits the FSOIs systems' ability to discern and accurately detect low-level optical signals. The presence of thermal noise can impact the sensitivity and signal-to-noise ratio (SNR) of the FSOIs systems, affecting the achievable data rate and overall system performance. Both channel-to-channel crosstalk and thermal noise impose limitations on the data rate and capacity of FSOI interconnects. These noise sources introduce errors, decrease the reliability of the transmitted data, and may require additional resources for error correction and mitigation [16; 17]. Managing and reducing these noise sources are critical considerations in the design and implementation of FSOI systems. By understanding and effectively managing noise sources, FSOI systems can achieve higher data rates, improved signal quality, and increased reliability, enabling their successful deployment in a wide range of applications that require fast and reliable wireless optical communication. Therefore, we investigate in this article the performance of FSOI systems employing the fundamental and higher-order transverse modes of operation with and without coding. In particular, the effect of using Reed-Solomon codes (RSCs) on improving the bandwidth density of free-space optical channels is discussed. We analyze the optimum coding gain capability for reducing the signal-to-noise (SNR) ratio required to achieve a desired bit error rate in the model operation. Section 2 presents a summary of the work related to the study of this article. In Section 3, we include both a design description for the used FSOI system model and a mathematical derivation for the normalized optical intensity of the considered modes of operation. Bandwidth density simulation results of an uncoded FSOI system are presented in Section 4. We provide in Section 5 the coding impact on the bandwidth density of the investigated modes along with numerical results. Finally, the conclusion and some ideas for future work are stated in Section 6.