  Over-complete systems of vectors, or in short, frames, play the role of
analog codes in many areas of communication and signal processing. To name a
few, spreading sequences for code-division multiple access (CDMA),
over-complete representations for multiple-description (MD) source coding,
space-time codes, sensing matrices for compressed sensing (CS), and more
recently, codes for unreliable distributed computation. In this survey paper we
observe an information-theoretic random-like behavior of frame subsets. Such
sub-frames arise in setups involving erasures (communication), random user
activity (multiple access), or sparsity (signal processing), in addition to
channel or quantization noise. The goodness of a frame as an analog code is a
function of the eigenvalues of a sub-frame, averaged over all sub-frames.
  Within the highly symmetric class of Equiangular Tight Frames (ETF), as well
as other "near ETF" families, we show a universal behavior of the empirical
eigenvalue distribution (ESD) of a randomly-selected sub-frame: (i) the ESD is
asymptotically indistinguishable from Wachter's MANOVA distribution; and (ii)
it exhibits a convergence rate to this limit that is indistinguishable from
that of a matrix sequence drawn from MANOVA (Jacobi) ensembles of corresponding
dimensions. Some of these results follow from careful statistical analysis of
empirical evidence, and some are proved analytically using random matrix theory
arguments of independent interest. The goodness measures of the MANOVA limit
distribution are better, in a concrete formal sense, than those of the
Marchenko-Pastur distribution at the same aspect ratio, implying that
deterministic analog codes are better than random (i.i.d.) analog codes. We
further give evidence that the ETF (and near ETF) family is in fact superior to
any other frame family in terms of its typical sub-frame goodness.
