AND-OR tree analysis of distributed LT codes

In this contribution, we consider design of distributed LT codes, i.e., independent rateless encodings of multiple sources which communicate to a common relay, where relay is able to combine incoming packets from the sources and forwards them to receivers. We provide density evolution formulae for distributed LT codes, which allow us to formulate distributed LT code design problem and prove the equivalence of performance of distributed LT codes and LT codes with related parameters in the asymptotic regime. Furthermore, we demonstrate that allowing LT coding apparatus at both the sources and the relay may prove advantageous to coding only at the sources and coding only at the relay.