21 research outputs found
A construction of strongly regular Cayley graphs and their applications to codebooks
In this paper, we give a kind of strongly regular Cayley graphs and a class of codebooks. Both constructions are based on choosing subsets of finite fields, and the main tools that we employed are Gauss sums. In particular, these obtained codebooks are asymptotically optimal with respect to the Welch bound and they have new parameters
On block coherence of frames
Block coherence of matrices plays an important role in analyzing the
performance of block compressed sensing recovery algorithms (Bajwa and Mixon,
2012). In this paper, we characterize two block coherence metrics: worst-case
and average block coherence. First, we present lower bounds on worst-case block
coherence, in both the general case and also when the matrix is constrained to
be a union of orthobases. We then present deterministic matrix constructions
based upon Kronecker products which obtain these lower bounds. We also
characterize the worst-case block coherence of random subspaces. Finally, we
present a flipping algorithm that can improve the average block coherence of a
matrix, while maintaining the worst-case block coherence of the original
matrix. We provide numerical examples which demonstrate that our proposed
deterministic matrix construction performs well in block compressed sensing