## 5 Conclusions  
In view of the difficulties of satellite communication information transmission, such as increasing environmental attenuation and dynamic time-varying links, this paper presents a new LDPC decoding algorithm based on multi-dimensional reliable information addition iteration that realizes a satellite communication system with a fast transmission rate and efficient decoding while ensuring the reliability of satellite link communication. The existing wtd-AlgB decoding algorithm involves frequent finite-field multiplication, and its performance needs to be improved. In the MRAI-LDPC algorithm, we design a subtraction operation to calculate the Hamming distance coefficient. Then, the channel received information is introduced for hard-decision and constellation mapping processing. The correlated reliability between the extrinsic information and the mapped processing information is designed to promote the correctness of decoding. Finally, an addition operation is used to obtain total reliability, avoiding real-field multiplication operations and reducing hardware complexity and power consumption. The simulation results show that the MRAI-LDPC algorithm outperforms about 0.4 dB in performance and has fast convergence performance compared with the wtd-AlgB algorithm. Meanwhile, the average number of iterations is reduced by 68% to improve the system's throughput. The MRAI-LDPC algorithm has better error-correcting performance to ensure the reliability of information transmission. Moreover, we believe that it has application value in future satellite high-speed data transmission systems. It is worth mentioning that more research is needed on efficiently implementing this algorithm on field-programmable gate arrays (FPGAs).  
Conceptualization, Y.H. and Y.W.; methodology, Y.H. and Y.W.; software, Y.W.; validation, Y.H. and Y.W.; formal analysis, Y.H. and Y.W.; investigation, Y.W.; resources, Y.H.; data curation, Y.W.; writing--original draft preparation, Y.W.; writing--review and editing, Y.H.; visualization, Y.W.; supervision, Y.H.; project administration, Y.H.; funding acquisition, Y.H. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Decoding Algorithm** & **RM** & **GA** & **GM** & **RA** & **RC** & **Total Operations** \\ \hline wtd-AlgB & 40,800 & 119,850 & 81,600 & 40,800 & 40,800 & 323,850 \\ Presented MRAI-LDPC & 0 & 80,580 & 32,640 & 65,280 & 23,460 & 201,960 \\ \hline \hline \end{tabular} Column weight: \(\rho=16\); row weight: \(\gamma=16\) (SNR of 4.6 dB).  
\end{table}
Table 4: Total complexities under the \(F_{16}(255,175)\) QC-LDPC code.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Decoding Algorithm** & **RM** & **GA** & **GM** & **RA** & **RC** & **Total Operations** \\ \hline wtd-AlgB & 28,350 & 83,025 & 56,700 & 28,350 & 28,350 & 224,775 \\ Presented MRAI-LDPC & 0 & 77,625 & 31,500 & 63,000 & 23,625 & 195,750 \\ \hline \hline \end{tabular} Column weight: \(\rho=14\); row weight: \(\gamma=14\) (SNR of 4.5 dB).  
\end{table}
Table 3: Total computational complexities of the \(F_{16}(225,147)\) QC-LDPC code.  
This research received no external funding.