# Performance of Adaptive Bit-Interleaved Polar Coded Modulation in FSOC System
## 2 Adaptive Bit-Interleaved Polar Coded Modulation (A-BIPCM)  
Construction of FSOC System and Channel Construction Based on Adaptive Bit-Interleaved Polar Code Encoding  
The proposed Principle block diagram of an FSOC system based on bit-interleaved polar code coding is illustrated in Figure 1. The system operates with an input source sequence of length \(k\), consisting of an information sequence and \(m\) cyclic redundancy check (CRC) transmission bits. The parallel sequences to be encoded are converted from serial to parallel format by the encoder. These sequences \(x_{1}^{N}=x_{1},x_{2},\cdots x_{N}\) undergo parallel polar coding, which is divided into \(r\) subchannels. The encoded sequences are then passed through an interleaver \(s(t)\), which reorders the bits to enhance error correction capabilities. The information sequence is divided into blocks with a length equal to the length of the interleaver according to the turbulence intensity. Adjacent bits of the coded bit sequence can be transmitted at intervals. After interleaving, the sequences are mapped and amplified using an erbium-doped optical fiber amplifier (EDFA). Subsequently, the amplified signals \(S(t)\) are transmitted through a fiber collimator (FC) into a fading channel. At the receiver end, the signal model is as follows:  
\[\mathrm{y(t)}=\eta\cdot I(\mathrm{t})\cdot S(\mathrm{t})+n(t) \tag{1}\]  
In this formula, the received signal is denoted by \(\mathrm{y(t)}\), which is the signal detected by the receiver. \(\eta\) represents the detector responsivity of the photodetector, and we assume that \(\eta\) is equal to one for simplicity. The transmitted signal is represented by \(S(t)\in\{0,1\}\). \(I(\mathrm{t})\) accounts for the intensity attenuation caused by atmospheric turbulence, which affects the received signal strength. \(n(t)\) represents the zero-mean Gaussian white noise experienced by the receiver, which contributes to the overall noise in the received signal. After receiving the signal, the received sequence undergoes demodulation and mapping processes. Subsequently, the deinterleaving operation is performed to reorder the sequence to its original order. The deinterleaved sequence is then delivered to the decoder [11]. In this work, we employ the Monte Carlo method to construct a simulation channel for atmospheric turbulence characterized by Gamma-Gamma random numbers. This model aims to provide a more precise depiction of the light propagation phenomena, encompassing both large-scale and small-scale irradiance fluctuations [12]. The Gamma-Gamma model employed in this research is defined as follows:  
\[f(\langle I\rangle)=\int_{0}^{\infty}\frac{2(\alpha\beta)^{\alpha+\beta/2}}{ \Gamma(\alpha)\Gamma(\beta)}\langle I\rangle^{\alpha+\beta/2-1}K_{\alpha- \beta}(2\sqrt{\alpha\beta\langle I\rangle})dI \tag{2}\]  
In the formula, normalization can be expressed as \(\langle\cdot\rangle\), and the normalized light intensity can be defined as \(\langle I\rangle=I/E(I)\)[13]. \(C_{n}^{2}\) represents the structural constants of the atmosphere. \(L\) represents the free space link distance, \(\kappa=2\pi/\lambda\) represents the space wave number, \(\lambda\) represents the wavelength of light, \(I\) represents the variable, and \(\Gamma(\cdot)\) is the gamma function. \(K_{\alpha-\beta}(\cdot)\) is the Bessel function of the second kind of \(\alpha-\beta\) order. \(\alpha\) and \(\beta\) are related to atmospheric conditions, which are given by:  
Figure 1: Schematic diagram of FSOC system with bit-interleaved polar coding modulation.