To address the performance degradation of Luby transform （LT） codes under Gaussian channels， where traditional robust soliton distribution （RSD） suffers from high decoding complexity and excessive overhead due to noise accumulation and redundancy in high-degree symbols， this paper proposes a dynamic coupled truncated distribution （DCTD）. The proposed distribution first dynamically truncates the RSD to suppress redundant high-degree symbols， thereby reducing computational complexity. It then introduces a pre-optimized fixed distribution to further sparsify the probability density in the medium-to-high degree region. To achieve an adaptive and smooth fusion of the two distributions， the Kullback-Leibler （KL） divergence is employed to quantitatively measure the statistical difference between the truncated RSD and the fixed distribution， based on which an adaptive switching point selection algorithm is designed. Furthermore， a nonlinear mixing strategy is developed， incorporating a sinusoidal modulation term to enhance the robustness of low-degree symbols and an exponential correction term to suppress redundant high-degree connections， ensuring a smooth transition and improved probability allocation across critical degree ranges. Simulation results demonstrate that at a code length of 1 000， DCTD reduces the average decoding overhead by 21.5% compared to RSD while maintaining the same decoding success rate. Additionally， the average degree is reduced by 29.90% to 46.49% across various code lengths， indicating a significant reduction in decoding complexity. These results confirm that DCTD achieves a better trade-off between decoding overhead， complexity and success rate， providing an effective degree distribution solution for LT codes in noise-limited scenarios.