Degree distribution optimization in Raptor network coding

We consider a multi-source delivery system, where Raptor coding at sources and linear network coding in overlay nodes work in concert for efficient data delivery in networks with diversity. Such a combination permits to increase throughput and loss resiliency in multicast scenarios with possibly multiple sources. The network coding operations however change the degree distribution in the set of packets that reach the receivers, so that the low complexity decoding benefits of Raptor codes are unfortunately diminished. We propose in this paper to change the degree distribution at encoder, in such a way that the degree distribution after network coding operations recovers a form that leads to low complexity decoding. We first analyze how the degree distribution of the encoded symbols is altered by network coding operations and losses in a regular network. Then we formulate a geometric optimization problem in order to compute the best degree distribution for encoding at sources, such that the decoding complexity is low and close to Raptor decoders´ performance. Simulations show that it is possible to maintain the low complexity decoding performance of Raptor codes even after linear network coding operations, as long as the coding at sources is adapted to the network characteristics.