Abstract: There are a large number of LT encoded packets with degree one which are copies of source information packets. An illegal recipient can intercept the information with part of the encoded packets even if the way of encoding is unknown. For this,the way of encoding of LT was modified. The packets with degree one is replaced with a pair packet of degree two and three. As the conventional BP algorithm can not decode this kind of codes, a BP-based decoding algorithm(D2BP) in which an extra processing for degree two packets is included was presented, while a complexity reduced Gaussian elimination decoding algorithm(SGE) is given. Simulations show that D2BP and SGE algorithms can successfully decode LT codes so that the degree one packets is deleted, and SGE algorithm has significantly higher decoding efficiency than BP and D2BP algorithms. The channel erasure has no influence on the decoding performance of SGE. Compared with traditional Gauss elimination algorithm, the complexity of SGE algorithm is obviously decreased.

Key words: LT codes, degree 2 belief propagation, sparse matrix, Gaussian elimination, information security