We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting bit-error probability as the length of the code goes to infinity via recent results in random hypergraphs by Darling and Norris, Ann. Appl. Probab., 2005. For a code of finite length, we provide an algorithm for computing the probability of block-error of the decoder. This algorithm improves by a linear factor the algorithm of Karp, Luby, and Shokrollahi, Proc. of ISIT, 2004.