A Low-Complexity Analysis of Finite-Length LT Codes Based on Degree Distribution Evolution

Luby Transform (LT) codes are key technologies to solve multiple access in future 6G wireless networks, and performance analysis is a significant part of such multiple access schemes. In this paper, we present a low-complexity performance analysis scheme for finite-length LT codes. First, matrix model is proposed to describe LT encode and belief-propagation (BP) decoder. Then, the degree distribution change during decoding is investigated based on the matrix model and the low-complexity performance analysis scheme is proposed. Numerical results show that the proposed analysis scheme significantly outperforms other schemes with low data length and precisely predicts the error probability of LT codes under the large or small overhead with high data length.