K-frame expansions with probabilistic erasures

In this paper, we use the K-frames to deal with the data erasures of communication. Firstly, we abstract the transmission as a Markov process. Then, we find and prove that we can use a K-frame with high redundancy to reconstruct signal with a high degree of accuracy. Secondly, we minimize the reconstruction as small as possible. Then, we establish a new probability model which is more practical in applications. And we use this model to deal with the date erasures. Furthermore, we construct a new K-frame named probability modeled Parseval K-frame. Finally, we use some numerical experiments to illustrate its advantages in date recover.