ANALYSIS OF THE PRINCIPLES OF IMPLEMENTING LUBY ERROR-CORRECTING CODES

DOI: 10.31673/2412-4338.2024.035461

Abstract

Packet-switched telecommunication networks are widely used for transmitting various types of information. However, the issue of packet loss significantly affects the quality of service for users. It has been shown that digital fountain codes are a popular class of erasure codes in the field of communication. Infinite encoded packets are continuously sent like a fountain, which is an important property of fountain codes, also known as rateless codes. Since the original data can be recovered regardless of which packets are received, fountain codes are also considered reliable for addressing the packet loss problem. It has been demonstrated that the modern approach to recovering lost packets involves the use of Luby codes, which represent the first practical foundation and implementation of fountain codes. These codes employ a special probability distribution law, which is a key characteristic in determining the efficiency of the code. The peculiarities of soliton-like probability distribution laws for Luby codes are considered. The main characteristics of these codes, which include efficiency, rateless coding, and reliability, are presented. Approaches to optimizing the codes based on Luby's transformation are analyzed. The principle of operation is shown, along with examples and features of the coding and decoding processes using Luby transformation codes. It is found that Luby transformation codes are a powerful tool for ensuring reliable and efficient data transmission in telecommunication systems. They enable high reliability even in challenging transmission conditions, making them extremely useful for modern telecommunication systems and networks. Finally, several approaches to optimizing the discussed codes in telecommunication systems are proposed. Optimizing Luby codes is a complex and multifaceted task that includes the use of various methods. However, the application of these methods can significantly enhance the efficiency and reliability of these codes in telecommunication systems.

Keywords: error-correcting codes, encoding, decoding, Luby codes, optimization.

References
1. Shtompel N.A. Bioinspired Optimization Method for Codes Based on Luby Transformation. Computer Science, Cybernetics, and Computer Engineering 2016. No. 2 (23), pp. 153-157.
2. Chen, C.-M., Chen, Y.-P., Shen, T.-C., Zao, J.K. Optimizing Degree Distributions in LT Codes by Using The Multiobjective Evolutionary Algorithm Based on Decomposition. NCLab Report No. NCL-TR-2010002 February 2010.
3. Ryan W., Lin. S. Channel Codes: Classical and Modern – New York: Cambridge University Press, 2009. – 674 p.
4. Luby, M. LT Codes. Proceedings of the 43rd Symposium on Foundations of Computer Science, IEEE Computer Society, 2002. – pp. 271 – 280.
5. Hyytia, E., Tirronen, T., Virtamo, J. Optimal Degree Distribution for LT Codes with Small Message Length. Proceedings of the 26th IEEE International Conference on Computer Communications (INFOCOM 2007), 2007. – pp. 2576 – 2580.
6. Asaulenko I.O., Prykhodko S.I., Shtompel M.A. Analysis of Data Recovery Methods in Packet-Switched Telecommunications Networks. Information and Control Systems in Railway Transport. 2015. – Issue 4. P. 27 – 38.
7. Bodine E.A., Cheng M.K. Characterization of Luby Transform Codes with Small Message Size for Low Latency Decoding. IEEE International Conference on Communications (ICC ’08), 2008. – pp. 1195 – 1199.
8. Shtompel N.A. Multi-criteria Optimization of Luby Codes Based on Natural Computations. Information and Control Systems in Railway Transport. 2017. – Issue 1. P. 24 – 27.
9. Joe Louis Paul I., Radha S., Raja J. Throughput and Bit Error Rate Analysis of Luby Transform Codes with Low and Medium Nodal Degree Distributions. American Journal of Applied Sciences 11 (9): 1584-1593, 2014.
10. Shtompel N.A. Trends in the Development of Methods for Interference-Resistant Coding of Information in Telecommunications. Communication, Radio Technology, Radar, Acoustics and Navigation. 2017. 1(50) P. 35-37.