In the domain of wireless communication systems, Error Control Coding (ECC) schemes are one of the widely relied upon or responsible methodology for securing the integrity and authenticity of the data transmission process. In the last decade, due to the advent of modern communication standards and their wide range of services, there has been a resurgence of interest and support in the research community towards the conception of efficient and versatile ECC techniques. Recent developments in the wireless communication based technologies have witnessed the pliable nature of low-density parity-check (LDPC) codes and their contributions which cannot be overstated. As of now, the decoding schemes based on LDPC codes have emerged as one of the most promising and effective coding scheme for addressing several key problems of reliable data communication. In this article, comprehensive overview on the current state-of-the art LDPC decoding algorithms and their applications are provided. In addition, a thorough investigation and comparison is carried out on various LDPC decoding algorithms based on their performance, similarities, scalability, numerical stability and feasibility for hardware realization. Finally, at the end of this review, views on the open research problems, challenges and the scope for future prospects are forecasted through discussions.

在无线通信系统的领域中，错误控制编码（ECC）方案是用于确保数据传输过程的完整性和真实性的广泛依赖或负责任的方法之一。在过去的十年中，由于现代通信标准的出现及其广泛的服务范围，研究界对有效和通用ECC技术的概念重新产生了兴趣和支持。基于无线通信的技术的最新发展已经见证了低密度奇偶校验（LDPC）码的柔韧性及其不可夸大的贡献。到目前为止，基于LDPC码的解码方案已经成为解决可靠数据通信的几个关键问题的最有希望和最有效的编码方案之一。在本文中，提供了有关当前最新的LDPC解码算法及其应用的全面概述。此外，基于各种LDPC解码算法的性能，相似性，可扩展性，数值稳定性和硬件实现的可行性，对其进行了深入的研究和比较。最后，在本次审查的最后，通过讨论预测了对开放研究问题，挑战和未来前景范围的看法。数值稳定性和硬件实现的可行性。最后，在本次审查的最后，通过讨论预测了对开放研究问题，挑战和未来前景范围的看法。数值稳定性和硬件实现的可行性。最后，在本次审查的最后，通过讨论预测了对开放研究问题，挑战和未来前景范围的看法。