# The Polar Code Construction Method in Free Space Optical Communication
## 1 Introduction  
Due to the advantages of a high transmission rate a large transmission capacity, and spectrum limitation, the free space optical (FSO) communication system [1; 2], is a popular research technology in application scenarios such as Last-mile technology, free space data backhaul and broadcasting [3; 4]. However, in the actual atmosphere laser communication link, the transmission of the laser beam in the atmospheric channel can be easily affected by the atmospheric turbulence effect and atmospheric attenuation effect [5]. Among them, random fluctuations in the amplitude and phase of the received signal caused by atmospheric turbulence [6] are the main factors leading to the deterioration of the performance of the communication system [7] and even have a great influence on the reliability of the communication system [8; 9]. Though adaptive optics [10], aperture averaging [11], spatial diversity [12], and modulation technique [13] have been used to suppress atmospheric turbulence effect and reduce the duration of fading, their high computational complexity and higher requirements for equipment have significantly increased the complexity and cost of the system [14; 15; 16]. Channel code technology has been proposed to resist the fading caused by atmospheric turbulence without changing the structure of the transmitter or receiver [17]. The common channel codes used in FSO communication include the Reed Solomon (RS) code [18], turbo code [19], and low-density parity check (LDPC) code [20], especially, and LDPC has the performance of approaching the Shannon limit [21]. However,in recent years, another coding scheme has come into the sight of researchers. It is the polar code proposed by Turkish professor [PERSON] in [22]. This scheme is the only error-correcting code that has been proved mathematically that reached the Shannon limit in binary discrete memoryless channel (B-DMC). In [23; 24], the authors investigated the performance of the polar code in the FSO system, and the result of the experiment showed that the polar code had a better error correction performance than the LDPC code in the turbulence channel. For the construction of polar code, in [22], [PERSON] proposed to construct the polar code by the Bhattacharyya parameter, while this method applied to the binary erasure channel (BEC). In order to extend polar codes to continuous output symmetrical channels, the authors in [25] introduced the density evolution (DE) method. However, a large number of convolution operations are involved in each density calculation, resulting in high computational complexity. To solve this problem, in [26], the Gaussian approximation (GA) method was proposed to evaluate the reliability of each component channel, which reduced the computational complexity to a linear correlation with code length, but this method was suitable for the additive white Gaussian noise (AWGN) channel. In 2016, [PERSON] [27] proposed the universal partial order (UPO) relationship among the sub-channels of polar code, which clearly provided the reliability relationship among some sub-channels. In [23], the Monte Carlo (MC) method was used to construct polar codes in the FSO system, but this method had a high complexity. This paper proposes the segmental turbulence partial order (STPO) method to improve the quality of laser communication by using polar code effectively, as well as to reduce the complexity of polar code construction in atmospheric strong turbulence channels. STPO combines the UPO, MC simulation, and polarization weight formula, among which UPO was used to determine the reliability of most component sub-channels, and the reliability of other sub-channels was determined by MC simulation in strong turbulence channels. Then, the polarization weight formula was combined to determine the optimal value of \(\beta\) in different signal-to-noise ratio (SNR) ranges, and the construction of the polar code sequence was completed according to the optimal value of \(\beta\) in the strong turbulence channel.