Degree Distribution of XORed Fountain Codes : Theoretical Derivation and Analysis
Résumé
In this work, we focus on the use of network coding in a wireless sensor network where data is already encoded at the source node with fountain codes, in particular LT or raptor codes. These codes have a specific degree distribution to follow in order to obtain an efficient decoding process. However, adding a layer of network coding on such packets triggers a distorsion of the degree distribution. Consequently, the packet overhead needed for the decoding process can grow significantly. In this paper, we analytically study how the degree distribution of the encoded packets evolves when they are XORed together. We prove that the degree distribution can be preserved if the degrees of the packets to be XORed are chosen according to a certain probability, that we define theoretically. Our results hold for any type of fountain codes, even if this paper presents results only for LT and Raptor codes.