Finite Length Analysis of Verifcation-Based Message Passing Algorithms in Compressed Sensing

Compressed sensing (CS) is a newly developed area in signal processing which generally aims at compressing sparse signals. The most challenging part of a CS problem can be the recovery process in which a signal will be reconstructed from its measurements. In this thesis, we address the finite length analysis of verification-based message-passing algorithms (VB MPAs), analytically. In contrary to asymptotic regime analysis, the finite length analysis is fairly an untouched problem. We begin the analysis by characterizing the problematic combinatorial structures, defined over the measurement graph of the CS system in which VB algorithms are trapped. Then, based on this characterization, we derive exact expressions for the average probability of error of a given ensemble of graphs, and also for a given individual graph. The analysis for the individual graph is also shown to be useful for the introduction and estimation of error floors in VB MPAs in CS.