A randomized algorithm and performance bounds for coded cooperative data exchange

We consider scenarios where wireless clients are missing some packets, but they collectively know every packet. The clients collaborate to exchange missing packets over an error-free broadcast channel with capacity of one packet per channel use. First, we present an algorithm that allows each client to obtain missing packets, with minimum number of transmissions. The algorithm employs random linear coding over a sufficiently large field. Next, we show that the field size can be reduced while maintaining the same number of transmissions. Finally, we establish lower and upper bounds on the minimum number of transmissions that are easily computable and often tight as demonstrated by numerical simulations.