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This paper proposes a Wyner-Ziv (WZ) switching scheme for multiple bit-rate (MBR) video streaming over networks. Identical video content is encoded into a set of normal streams, which are generated by conventional hybrid video coding with multiple bit rates, so that streaming can dynamically switch among these normal streams according to available bandwidth. At encoder side, the WZ codec generates a switching stream by compressing the reconstructed frames of a certain normal stream that will be switched to, no matter which normal stream it switches from. At decoder side, for switching to the same frame, the same WZ switching stream is used to reconstruct the switching-to frame by taking the switching-from frame as the side information. The number of required WZ bits depends on the inherent mutual correlation between two frames switching to and from. Since the WZ switching streams are generated independently of the normal switching-from streams, given normal streams that can switch from any one to another, the proposed scheme reduces the number of switching streams from to . Furthermore, switching streams do not deteriorate the coding efficiency of normal streams when no switching occurs. However a big problem here, similar to requesting bits in distributed video coding, is how many WZ bits should be transmitted when a switching happens because the streaming scenario does not tolerate too much extra delay caused by the requests back and forth. Therefore, a Laplacian model, which is proved in the simplified case, is proposed to characterize the correlation between switching-to and switching-from frames. It can be used to accurately estimate the number of WZ bits at the server side.