Frames of uniform subframe bounds with applications to erasures

We introduce a class of frames, called USB frames (frames of uniform subframe bounds), which mean that any subsequence of the frame is a frame for the subspace it spans and the frame bounds depend only on the cardinality of the subsequence. We give several necessary and sufficient conditions for a frame to be a USB frame. As an application, we show that a tight USB frame is optimal for erasures in the sense that the reconstruction error is independent of the position of erasures. We give several explicit construction of USB frames.