On the spectral distribution of a deterministic matrix constructed from linear codes
by Enoch Kung
THESIS
2014
M.Phil. Mathematics
vii, 38 pages : illustrations ; 30 cm
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.
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