Mendoza Smith, Rodrigo and Tanner, Jared (2015) Expander Decoding. Technical Report. Unspecified. (Submitted)

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Abstract
We introduce two new algorithms, Serial and Parallel for solving a large underdetermined linear system of equations when it is known that has at most nonzero entries and that is the adjacency matrix of an unbalanced left regular expander graph. The matrices in this class are sparse and allow a highly efficient implementation. A number of algorithms have been designed to work exclusively under this setting, composing the branch of combinatorial compressedsensing (CCS).
Serial and Parallel iteratively minimise by successfully combining two desirable features of previous CCS algorithms: the informationpreserving strategy of ER, and the parallel updating mechanism of SMP. We are able to link these elements and guarantee convergence in operations by assuming that the signal is , meaning that all of the subset sums of the support of are pairwise different. However, we observe empirically that the signal need not be exactly dissociated in practice. Moreover, we observe Serial and Parallel to be able to solve large scale problems with a larger fraction of nonzeros than other algorithms when the number of measurements is substantially less than the signal length; in particular, they are able to reliably solve for a sparse vector from expander measurements with and up to four times greater than what is achievable by regularization from dense Gaussian measurements. Additionally, due to their low computational complexity, Serial and Parallel are observed to be able to solve large problems sizes in substantially less time than other algorithms for compressed sensing. In particular, Parallel is structured to take advantage of massively parallel architectures.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1901 
Deposited By:  Helen Taylor 
Deposited On:  17 Sep 2015 06:52 
Last Modified:  17 Sep 2015 06:52 
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