Analog Source Coding and Robust Frames

Ram Zamir
Professor, Tel Aviv University
Date: Mar. 9th, 2018


Analog (Discrete Fourier Transform) codes use redundancy in the spectral domain to gain immunity against channel erasures, or to compress a source under an erasure distortion measure. A robust analog code amounts to an over-complete basis (a frame), whose subset singular-value distribution is typically narrow. We show that if we form a basis by selecting DFT frequencies form a difference set, then we obtain an equiangular tight frame (ETF), whose asymptotic subset singular-values have a MANOVA distribution. This implies that the noise amplification of the resulting DFT code is significantly lower than that obtained using band-limited interpolation or random (Gaussian) frames. Furthermore, the gap from the quadratic-Gaussian rate-distortion function is bounded by about 0.5 bit at moderate signal to distortion ratios.

Joint work with Marina Haikin (Tel Aviv University) and Matan Gavish (HUJI).