We consider a network where multiple sources communicate via a single relay to sinks with non-uniform and unequal demands. The LT distributions employed at the sources may be ill-matched to the demands of the sinks connected to the relay. We consider a probabilistic “morphing” of two or more fountain-encoded streams into a single stream better suited for the demand patterns downstream of the relay. The relay observes symbols generated from two distinct fountain codes, and can decide to forward a symbol from one source, or the other source, or the X-OR of the two symbols. We propose a linear programming based design of Generalized LT codes, which with appropriate substitutions is utilized to design the probabilities for the relay. Simulation results show that the designs obtained on the basis of the proposed optimization problem, when compared with multiplexing or simple mixing, reduce the number of symbols that have to be downloaded to guarantee a desired probability of successful decoding.
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