Polar Code BP Decoding Optimization for Green 6G Satellite Communication: A Geometry Perspective

The rapid evolution of mega-constellation networks and 6G satellite communication systems has ushered in an era of ubiquitous connectivity, yet their sustainability is threatened by the energy-computation dilemma inherent in high-throughput data transmission. Polar codes, as a coding scheme capable of achieving Shannon's limit, have emerged as one of the key candidate coding technologies for 6G networks. Despite the high parallelism and excellent performance of their Belief Propagation (BP) decoding algorithm, its drawbacks of numerous iterations and slow convergence can lead to higher energy consumption, impacting system energy efficiency and sustainability. Therefore, research on efficient early termination algorithms has become an important direction in polar code research. In this paper, based on information geometry theory, we propose a novel geometric framework for BP decoding of polar codes and design two early termination algorithms under this framework: an early termination algorithm based on Riemannian distance and an early termination algorithm based on divergence. These algorithms improve convergence speed by geometrically analyzing the changes in soft information during the BP decoding process. Simulation results indicate that, when Eb/N0 is between 1.5 dB and 2.5 dB, compared to three classical early termination algorithms, the two early termination algorithms proposed in this paper reduce the number of iterations by 4.7-11% and 8.8-15.9%, respectively. Crucially, while this work is motivated by the unique demands of satellite networks, the geometric characterization of polar code BP decoding transcends specific applications. The proposed framework is inherently adaptable to any communication system requiring energy-efficient channel coding, including 6G terrestrial networks, Internet of Things (IoT) edge devices, and unmanned aerial vehicle (UAV) swarms, thereby bridging theoretical coding advances with real-world scalability challenges.