Abstract: Concerning the problem that the performance analysis method of Luby Transform (LT) codes under Gaussian elimination decoding algorithm is complicated and inaccurate, a novel performance analysis method based on probability transfer function was proposed. Firstly, for two LT codes with simple uniform degree distribution, the precise performance was studied and its quantitative expression was given. Secondly, the general LT code was investigated, and a simple but effective qualitative analysis method was proposed. Finally, the simulation work was done to verify the new method. In the comparison experiments with the traditional method which only gives the upper and the lower bounds of the rank of generated matrix, the maximum error of performance analysis results for simple uniform degree LT codes reduces to 0.0124, and the complexity of general LT codes decrease to O(k²). Theoretical analysis shows that the proposed method can effectively guide the optimization design of LT codes in communication area.

Key words: digital fountain, Luby Transform (LT) code, degree distribution, Gaussian elimination, performance analysis

摘要： 针对LT码在采用高斯消元算法时性能分析方法计算复杂且性能较差这一问题，提出了基于概率转移函数的性能分析方法。首先，对两种均匀度分布下的LT码进行了分析并给出了性能的定量表达式；其次，研究了一般性度分布下LT码，给出了一种简单有效的性能衡量的指标参数，并给出了参数的计算表达式；最后，对提出的性能分析方法进行了仿真验证分析。仿真结果表明，与基于生成矩阵满秩上下界计算方法相比较，基于概率转移函数方法对于均匀度分布码字的性能衡量最大误差降低到0.0124，一般码字计算复杂度降低到O（k²）。理论分析表明，基于概率转移方法能够更有效地指导通信领域LT码的优化设计。

关键词: 数字喷泉, LT码, 度分布, 高斯消元, 性能分析