The introduction of sixth-generation mobile communication technology (6G) poses new requirements for the capacity, rate, latency, and reliability of communication systems. As a vital component of 6G technology, unmanned aerial vehicle (UAV) communications also face various challenges, such as noise interference and limited hardware resources. To meet the high demands of 6G, advanced channel coding techniques need to be adopted. Polar codes, due to their theoretically achievable Shannon limit performance, have potential applications in UAV communication systems. Constructing reliable polar decoding schemes is currently a research hotspot in the field of communications. The Belief Propagation List (BPL) decoding algorithm for polar codes can effectively enhance the accuracy of polar code BP decoding. However, existing BPL decoding algorithms for polar codes face issues such as high hardware resource consumption and unsatisfactory decoding accuracy. Addressing the aforementioned issues, this paper proposes a BPL decoding algorithm for polar codes based on information geometry. An information geometry framework is constructed, where the soft information output by the BP decoder is treated as points on a statistical manifold, and their geometric properties are calculated. By introducing the concept of the soft information centroid and a path selection criterion based on the soft information centroid, combined with geometric distance as a weight, the decoding performance is improved, and hardware overhead is reduced. Simulation results show that under the conditions of a maximum of 60 iterations and 5 decoders, the proposed algorithm reduces the bit error rate by 16.2–74.9% compared to the classic BPL algorithm, providing strong technical support for the application of polar codes in scenarios such as UAV communications.
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