## 1 Introduction  
In the rapidly evolving landscape of information technology, from smart homes to industrial automation, and from health and medical applications to intelligent transportation systems, the extensive application of Internet of Things (IoT) devices is becoming increasingly critical. These devices depend on efficient and reliable data transmission technologies to ensure the accuracy and timeliness of their operations [1]. Particularly with the support of modern communication technologies such as 6G, the efficiency and accuracy of data transmission are directly linked to the overall performance and security of the system [2, 3]. The CRC is a prevalent error detection method that employs a specific polynomial to generate check bits, thereby enabling the detection of errors during data transmission. Polar Codes, a novel approach to channel coding, have been incorporated into the 5G standard, primarily because of their signal-to-noise ratio (SNR) and their straightforward structure. Moreover, the enhanced polarized codes are capable of fulfilling the demands for high-capacity and high-reliability transmission in the context of 6G [4, 5, 6, 7]. The core of the 3G error correction method is to reduce the transmission error rate through forward error correction (FEC) technology, thereby optimizing network throughput [8]. The 4G error correction method uses turbo code and LDPC code close to the Shannon limit to efficiently achieve a lower bit error rate (BER) and higher data transmission rate, while taking into account the optimization of decoding complexity [9]. The 5G error correction method uses efficient LDPC code and Polar Code, and achieves high error correction capability and flexible adaptation to the transmission requirements of code rate and length through soft decision technology [10]. The 6G error correction method emphasizes the development of advanced channel coding technology that adapts to high-frequency communication, low latency, high reliability and multi-objective optimization requirements, including LDPC, Polar Code, turbo code and their variants, and uses various methods to optimize performance [11]. From 1G to 6G, channel coding has experienced an evolution from analog transmission to digitalization, the introduction of error correction coding, and the realization of ultra-high data rates and low-latency communication. In 6G, more efficient coding technology will be used to meet the future requirements of extremely high reliability, low power consumption, and massive connections [12]. Polar Codes, a recent development in channel coding, have attracted considerable attention due to their theoretical potential to approach channel capacity and their relatively low encoding and decoding complexity [13]. They have been selected as the coding method for the 5G enhanced Mobile Broadband (eMBB) use case and the Physical Broadcast Channel (PBCH) [14; 15]. Among the various decoding strategies for Polar Codes, Successive Cancellation Decoding (SC) [13], Successive Cancellation List Decoding (SCL) [16], and Belief Propagation Decoding (BP) [17] are the most widely employed, each offering a different trade-off between performance and complexity, highlighting the versatility of Polar Codes in various communication scenarios. SC decoding is characterized by its low complexity but is outperformed by SCL decoding, which improves decoding performance by maintaining multiple potential paths at a higher complexity. BP decoding, which employs iterative propagation, can provide better performance at lower SNRs but may suffer from convergence issues and stability problems. [PERSON] et al. [18] reviewed the basic concepts and decoding algorithms of polarized codes, demonstrating the potential to outperform turbo and LDPC codes, but the use of polarized codes alone resulted in decoding performance and channel applicability that are not applicable to future 6G communication systems, but the use of only Polar coding did not perform well enough in terms of channel applicability. [PERSON] et al.