  In modern communication systems such as the Internet, random losses of
information can be mitigated by oversampling the source. This is equivalent to
expanding the source using overcomplete systems of vectors (frames), as opposed
to the traditional basis expansions. Dependencies among the coefficients in
frame expansions often allow for better performance comparing to bases under
random losses of coefficients. We show that for any n-dimensional frame, any
source can be linearly reconstructed from only (n log n) randomly chosen frame
coefficients, with a small error and with high probability. Thus every frame
expansion withstands random losses better (for worst case sources) than the
orthogonal basis expansion, for which the (n log n) bound is attained. The
proof reduces to M.Rudelson's selection theorem on random vectors in the
isotropic position, which is based on the non-commutative Khinchine's
inequality.
