A Novel Variable-Order Threshold Serial Belief Propagation-Based Decoding Algorithm for LT Codes

The belief propagation (BP) algorithm is a widely adopted iterative decoding method for Luby transform (LT) codes. However, the conventional log-likelihood ratio BP (LLR-BP) decoder exhibits inherent limitations in additive white Gaussian noise (AWGN) channels. These limitations include high computational complexity, slow convergence speed, and limited decoding efficiency. To address these challenges, we propose a variable-order threshold serial belief propagation (VOT-SBP) algorithm. The proposed algorithm integrates the serial belief propagation (SBP) method with a reliability metric for check nodes, enabling accurate determination of the sequence for message updates. In addition, by introducing an adaptive threshold for correcting check node information, the algorithm effectively eliminates redundant update actions throughout the decoding process. Simulation results demonstrate a 63.6% reduction in iteration count compared to BP for long-length codes at medium to high signal-to-noise ratio (SNR) and a 17.4% decrease in computational overhead. This approach enhances both decoding performance and convergence efficiency.