  Analog coding is a low-complexity method to combat erasures, based on linear
redundancy in the signal space domain. Previous work examined "band-limited
discrete Fourier transform (DFT)" codes for Gaussian channels with erasures or
impulses. We extend this concept to source coding with "erasure
side-information" at the encoder and show that the performance of band-limited
DFT can be significantly improved using irregular spectrum, and more generally,
using equiangular tight frames (ETF). Frames are overcomplete bases and are
widely used in mathematics, computer science, engineering, and statistics since
they provide a stable and robust decomposition. Design of frames with favorable
properties of random subframes is motivated in variety of applications,
including code-devision multiple access (CDMA), compressed sensing and analog
coding. We present a novel relation between deterministic frames and random
matrix theory. We show empirically that the MANOVA ensemble offers a universal
description of the spectra of randomly selected subframes with constant aspect
ratios, taken from deterministic near-ETFs. Moreover, we derive an analytic
framework and bring a formal validation for some of the empirical results,
specifically that the asymptotic form for the moments of high orders of subsets
of ETF agree with that of MANOVA. Finally, when exploring over-complete bases,
the Welch bound is a lower bound on the root mean square cross correlation
between vectors. We extend the Welch bound to an erasure setting, in which a
reduced frame, composed of a random subset of Bernoulli selected vectors, is of
interest. The lower bound involves moment of the reduced frame, and it is tight
for ETFs and asymptotically coincides with the MANOVA moments. This result
offers a novel perspective on the superiority of ETFs over other frames.
