Frame expansions with probabilistic erasures

In modern communication network such as a public Internet, random losses of information can be recovered by frame expansions. In this paper, we think about the transport protocol that delivers a coefficient of frame expansions with some probability of failure via multiple intermediate nodes. By this protocol, we abstract the transmission as a Markov process. In this case, even if the probabilities of erasures are close to the 1/2, we show that the reconstruction error can be minimized as small as possible by using frames with high redundancy. Furthermore, we set up a probability model for constructing optimal Parseval frames that are robust to one probabilistic erasure. It is shown that probabilistic modeled Parseval frames are more effective than traditional Parseval frames on recovering the signal with probabilistic erasures.