Cyclic redundancy check (CRC) is an important channel coding technique used to detect possible errors in data transmission or storage. This article conducts an in-depth discussion of the principles and applications of CRC, and focuses on the method of parallel CRC calculation. First, this paper discussed the basic role of CRC in communication systems and its relationship with channel coding technology. Subsequently, this paper introduced the research results of several existing parallel CRC algorithms, including the PQC-CRC method and the CRC algorithm based on multi-level parallelism. These methods take advantage of the parallel performance of modern processors to improve the efficiency and speed of CRC calculations. This paper also discussed the importance of parallel CRC calculations in large-scale data environments, and proposed prospects for future research, including application prospects in the fields of high-performance computing, the Internet of Things, 5G, and new hardware architectures. Through the research in this article, this paper hopes to provide useful references and inspirations for improving the performance of data transmission and storage systems and meeting future communication and computing needs.