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The central topic of this paper is the linear, redundant encoding of vectors using frames for the purpose of loss-insensitive data transmission. Our goal is to minimize the reconstruction er- ror when frame coecients are accidentally erased. Two-uniform frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest Euclidean error norm when up to two frame coecients are set to zero. Here, we consider the case when an arbitrary number of the frame coecients of a vector is lost. We derive general error bounds and apply these to concrete examples. We show that among the 227 known equiva- lence classes of two-uniform (36,15)-frames arising from Hadamard matrices, there are 5 that give smallest error bounds for up to 8 erasures.

Loss-insensitive vector encoding with two-uniform frames