## 1 Introduction  
With the vigorous development of sixth-generation mobile communication (6G) technology, unmanned aerial vehicle (UAV) communication, as an indispensable potential technology within it, is gradually demonstrating its unique advantages and broad application prospects. UAVs, as small aircraft, play a vital role in achieving airspace coverage in the global three-dimensional deep coverage of \"space, air, ground, and sea\" envisioned for 6G, thanks to their multifunctionality, high mobility, ease of deployment, and low cost [1]. Serving as an airspace-assisted communication platform, UAVs can fill in the blind spots of traditional communication networks, provide stable and efficient communication services, and offer robust support for communication needs in remote areas, emergency scenarios, and complex terrains. However, UAV communication also faces numerous challenges, such as noise interference and limited hardware resources, which raise higher requirements for the performance of communication systems. The advent of 6G technology poses unprecedented challenges to the capacity, rate, latency, and reliability of communication systems [2]. To address these challenges, advanced technologies such as signal processing, spectrum management, and channel coding can be employed to enhance the performance of communication systems. Among them, channel coding technology is one of the key technologies for UAV communication in 6G due to its ability to significantly improve communication reliability and stability. Polar codes, a coding scheme proposed by [PERSON] based on polarization theory, are the first coding method theoretically proven to achieve the Shannon limit [3]. Their excellent coding performance and low complexity give polar codes broad application potential in UAV communication systems. Especially in scenarios with high-speed UAV movement and complex and changing channel conditions, polar codes can demonstrate their powerful error correction capability and stability, ensuring the continuity and reliability of communication. To meet the high requirements of 6G for UAV communication systems, efficient decoding methods are needed to fully leverage the advantages of polar codes. In terms of polar code decoding, there are mainly two approaches: Successive Cancellation (SC) decoding and Belief Propagation (BP) decoding. Among them, the BP algorithm, characterized by its high-throughput decoding and high parallelism, favors hardware implementation. As a soft-input soft-output decoding algorithm, it is suitable for application in iterative detection and decoding systems. [PERSON] proposed a BP polar decoding algorithm based on message propagation in references [3; 4] and further provided iterative formulas for BP decoding in reference [5], highlighting the superiority of BP decoding. The BP decoding algorithm not only improves decoding speed but also maintains high decoding accuracy in complex and changing UAV communication environments, providing robust support for the reliability of UAV communication. However, a major drawback of BP decoding is its relatively poor error correction performance. Even after sufficient iterations, the decoding accuracy of the BP decoding algorithm is only slightly higher than that of the SC decoding algorithm and inferior to the Successive Cancellation List (SCL) decoding algorithm and various enhanced SC decoding algorithms. [PERSON] et al. found in reference [6] that permutation factor graphs can improve BP decoding algorithms and later proposed a decoding algorithm called Belief Propagation List (BPL) in reference [7], which uses multiple factor graphs for decoding and complements the decoding results to achieve similar decoding performance to SCL. The BPL decoding process is as follows: Firstly, the signal y received from the channel end is input into \(L\) independent BP decoders (with different factor graphs) for decoding, yielding \(L\) decoding results.