On the spectral distribution of a deterministic matrix constructed from linear codes

Abstract

This work is partly motivated by the study of compressed sensing, which deals with the sampling and recovery of signals. Calderbank etal (2010) proved that a large class of deterministic matrices arising from linear codes satisfy the Statistical Isometry Property, an important property desired in compressed sensing. In this paper, we prove that more is true: such matrices behave like random matrices in the sense that the Gram matrix of randomly chosen submatrices possesses a spectral distribution that converges to the Wigner's semicircle distribution.

Date of Award	2014
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology