# Investigation of IEEE 802.16e LDPC Code Application in PM-DQPSK System
## 3 PM-DQPSK System and Simulation Results
### Simulation Results  
In this paper, following the compensation module mentioned above, LDPC is integrated into the PM-DQPSK coherent optical transmission system. Specifically, the LDPC decoding algorithm further processes the recovered data obtained from the symbol judgment module, enhancing the overall performance of the system. The primary aim is to evaluate the effectiveness of LDPC in improving the quality and reliability of the transmitted data. Through a comparative analysis, the results from the comparison provide significant findings regarding the benefits and potential improvements that LDPC can provide in the PM-DQPSK coherent optical transmission system. This study seeks to elucidate the benefits and potential enhancements LDPC can provide within the context of the PM-DQPSK coherent optical transmission system. To facilitate this evaluation, the parameters of the PM-DQPSK simulation system are configured as follows in Table 1.  
Figure 2: Digital signal processing compensation flowchart. The system incorporates LDPC codes based on the IEEE802.16e standard, employing both the fast iterative coding algorithm and the BP decoding algorithm. These elements play pivotal roles in ensuring robust data transmission and error correction. Detailed parameter settings can be found in Table 2.  
In order to ensure the effectiveness of the simulation, the control variables were carried out. Firstly, the different maximum numbers of iterations were changed for simulation, and the influence of different maximum numbers of iterations on error correction performance was compared. When adjusting the number of iterations, the LDPC configurations maintained consistent code length, code rate and number of encodings. Upon determining the optimal maximum number of iterations, simulations were conducted using LDPC codes of various lengths as specified in the IEEE802.16e standard. Specifically, the number of encodings corresponding to code lengths of 576, 1152, and 2304 are 800, 400, and 200. The noise figure (NF) and OSNR are intimately related parameters in optical communication systems, particularly in receiver performance evaluation. NF quantifies the degradation of the OSNR introduced by electronic devices like amplifiers or receivers, with lower values indicating less noise contribution and better receiver sensitivity. On the other hand, OSNR measures the ratio of optical signal power to noise power in the system, reflecting signal quality relative to noise. There exists an inverse relationship between NF and OSNR: lower NF corresponds to higher sensitivity and improved OSNR, while higher NF results in decreased sensitivity and reduced OSNR. Adjusting the NF to manipulate the OSNR simulates attenuation damage and obtains different BER. BP iterative decoding algorithm makes LDPC codes exhibit excellent performance. The decoding performance of LDPC code is affected by the number of iterations. When the number of iterations is small, the decoding information is still in unstable bagging, so it is necessary to increase the number of iterations, constantly accumulate more information, and improve the accuracy of the decoded message. The performance of the LDPC algorithm is assessed across various iteration counts. This paper selects 5, 10, 15, and 20 iterations for BER simulation analysis. As illustrated in Figure 3, the findings demonstrate an enhancement in decoding performance with an increase in the number of iterations. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline Length of fiber & 100 km \\ Transmission rate & 40 Gbps \\ Output average power & \(1.0\times 10^{-3}\) W \\ Laser linewidth & 100 kHz \\ PMD coefficient & 0.2 ps/km\({}^{1/2}\) \\ CD coefficient & 16 ps/nm/km \\ Attenuation coefficient & 0.2 dB/km \\ Effective core area & \(80.0\times 10^{-12}\) m\({}^{2}\) \\ Semiconductor Optical Amplifier gain & 20 dB \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters setting of PM-DQPSK simulation system.