On the Spark of Binary LDPC Measurement Matrices From Complete Protographs

Abstract

The spark is an important property that provides recovery guarantees of a measurement matrix in compressed sensing. In this letter, we focus on a specific class of measurement matrices, i.e., binary low-density parity-check (LDPC) matrices from complete protographs. An upper bound on the spark of a binary LDPC measurement matrix from complete protograph is provided. In addition, the spark of array-based LDPC measurement matrices with certain column weights is analyzed.