Optimizing the Degree Distribution of LT codes with an Importance Sampling Approach

Fountain coding principle introduced by Byers et al. in 1998 describes an efficient way to transfer information over erasure channels. In this paper, we focus on a particular class of fountain codes, the LT codes. The key component of LT codes is the so-called degree distribution used in the encoding procedure. The degree distribution is the sole component responsible for the efficiency of the LT codes. In general, the optimization of the degree distribution is not a trivial problem. This paper describes an algorithm for iterative optimization of parameterized degree distributions for LT codes. In particular, we use methods utilized in importance sampling theory to construct an objective function which eventually is optimized with non-linear optimization methods. The proposed method is studied for message lengths of a couple of hundred blocks and less. We present some examples of degree distributions optimized with the proposed algorithm with comparisons to the performance of previously proposed distributions.