On the optimization of degree distributions in LT code with covariance matrix adaptation evolution strategy

Luby Transform code (LT code) has been a popular and practical technique in the field of channel coding since its proposal. One of the key components of LT code is a degree distribution which is used to determine the relationship between source data and codewords. Luby in his proposal suggested two general methods to construct feasible degree distributions. Such general designs work appropriately in typical situations but not optimally in most cases. To explore the full potential of LT code, in this work, we make the first attempt to introduce evolutionary algorithms to optimize the degree distribution in LT code. Degree distributions are encoded as real-valued vectors and evaluated by numerical simulation of LT code. For applications of different natures, two objectives are implemented to search good degree distributions with different decoding behavior. Compared with the original design, the experimental results are quite promising and demonstrate that the degree distribution can be customized for different purposes. In addition to manually adjusting the degree distribution as the common practice, the work presented in this paper provides an efficient alternative approach to use and adapt LT code for both practitioners and researchers.