Cooperative diversity has emerged as a promising technique to combat fading in wireless communications (Sendonaris et. al., 2003a; Sendonaris et. al., 2003b). It is based on the broadcast nature of the wireless medium and enables single-antenna users to “enjoy” space diversity benefits by sharing their physical resources through a virtual transmit and/or receive antenna array. The basic relay c...

We consider the problem of amplifying the “lossiness” of functions. We say that an oracle circuit C∗ : {0, 1} → {0, 1}∗ amplifies relative lossiness from `/n to L/m if for every function f : {0, 1} → {0, 1} it holds that 1. If f is injective then so is C . 2. If f has image size of at most 2n−`, then C has image size at most 2m−L. The question is whether such C∗ exists for L/m `/n. This problem...