Sub-linear time compressed sensing for support recovery using left and right regular sparse-graph codes - Vem, Avinash; Janakiraman, Nagaraj Thenkarai; Narayanan, Krishna (2016 IEEE Information Theory Workshop (ITW), 2016)
In [1], [2], two schemes have been proposed to recover the support of a K-sparse N-dimensional signal from noisy linear measurements. Both schemes use left-regular sparse-graph code based sensing matrices and a simple peeling-based decoding algorithm. Both the schemes require O(K logN) measurements and the first scheme require O(N logN) computations whereas the second scheme requires O(K logN) computations (sub-linear time complexity when K is sub-linear in N). We show that by replacing the left-regular ensemble with left and right regular ensemble, we can reduce the number of measurements required of these schemes to the optimal order of O(K log N/K) with decoding complexities of O(K log N/K) and O(N log N/K), respectively.