By Topic

Spectral Distribution of Product of Pseudorandom Matrices Formed From Binary Block Codes

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Babadi, B. ; Dept. of Anesthesia, Critical Care, & Pain Med., Massachusetts Gen. Hosp., Boston, MA, USA ; Tarokh, V.

Let A ∈ {-1,1}Na ×n and B ∈ {-1,1}Nb ×n be two matrices whose rows are drawn i.i.d. from the codewords of the binary codes Ca and Cb of length n and dual distances d'a and d'b, respectively, under the mapping 0 → 1 and 1 → -1. It is proven that as n → ∞ with ya:=n/Na ∈ (0,∞) and yb:=n/Nb ∈ (0, ∞) fixed, the empirical spectral distribution of the matrix A B*/√{Na Nb} resembles a universal distribution (closely related to the distribution function of the free multiplicative convolution of two members of the Marchenko-Pastur family of densities) in the sense of the Lévy distance, if the asymptotic dual distances of the underlying binary codes are large enough. Moreover, an explicit upper bound on the Lévy distance of the two distributions in terms of ya, yb, d'a, and d'b is given. Under mild conditions, the upper bound is strengthened to the Kolmogorov distance of the underlying distributions. Numerical studies on the empirical spectral distribution of the product of random matrices from BCH and Gold codes are provided, which verify the validity of this result.

Published in:

Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 2 )