Improved online fountain codes based on shaping for left degree distribution

In this paper, an improved encoding scheme for online fountain codes is proposed with the joint optimization of variable node degree and check node degree is proposed. The coding scheme can be divided into the build-up phase and the completion phase. In the build-up phase, left degree distribution is exploited to guarantee optimal performance phase by modifying the traditional coding scheme of choosing input symbols uniformly at random. A memory-based selecting of the source symbols is employed to decrease the number of connected components, which can thus produce the dimension increasement of the linear subspace of a decoding graph constructed in the build-up phase. The upper bound on coding overhead is also derived from the analysis of random graph theory. Compared with conventional online fountain codes, it can be seen from the simulation results that the proposed scheme can provide significant performance improvement with respect to both coding overhead and feedback cost. Moreover, the lower encoding/decoding complexities may make the proposed scheme more practical in energy-constrained applications such as distributed storage.