Density Evolution Analysis of Node-Based Verification-Based Algorithms in Compressed Sensing

In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recovery algorithms in the context of compressed sensing. These algorithms are particularly interesting due to their low complexity (linear in the signal dimension n ). The asymptotic analysi...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 58; no. 10; pp. 6616 - 6645
Main Authors: Eftekhari, Y., Heidarzadeh, A., Banihashemi, A. H., Lambadaris, I.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Asymptotic analysis
Asymptotic methods
Asymptotic properties
channel coding
Coding, codes
Compressed sensing
Data compression
Decoding
Density
density evolution
Detection
Differential equations
Exact sciences and technology
Information theory
Information, signal and communications theory
iterative decoding algorithms
iterative recovery algorithms
low-complexity compressed sensing
low-density parity-check (LDPC) codes
Mathematical analysis
Mathematical models
Matrix
message-passing algorithms
Niobium
Recovery
Sampling, quantization
Sensors
Signal and communications theory
Simulation
sparse graphs
Sparse matrices
sparse sensing matrix
success threshold
Telecommunications and information theory
verification-based recovery algorithms
Performance evaluation
iterative recovery algorithms
Input signal
Differential equation
Iterative method
iterative decoding algorithms
Iterative decoding
Implementation
low-density parity-check (LDPC) codes
Sparse matrix
Parity check codes
Asymptotic analysis
Deterministic approach
verification-based recovery algorithms
Large scale system
Target tracking
sparse graphs
density evolution
low-complexity compressed sensing
Algorithm
Channel coding
success threshold
message-passing algorithms
Message passing
Simulation
Concentration effect
Error correcting code
sparse sensing matrix
Compressed sensing
ISSN:0018-9448, 1557-9654
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Summary:In this paper, we present a new approach for the analysis of iterative node-based verification-based (NB-VB) recovery algorithms in the context of compressed sensing. These algorithms are particularly interesting due to their low complexity (linear in the signal dimension n ). The asymptotic analysis predicts the fraction of unverified signal elements at each iteration l in the asymptotic regime where n →∞. The analysis is similar in nature to the well-known density evolution technique commonly used to analyze iterative decoding algorithms. To perform the analysis, a message-passing interpretation of NB-VB algorithms is provided. This interpretation lacks the extrinsic nature of standard message-passing algorithms to which density evolution is usually applied. This requires a number of nontrivial modifications in the analysis. The analysis tracks the average performance of the recovery algorithms over the ensembles of input signals and sensing matrices as a function of l . Concentration results are devised to demonstrate that the performance of the recovery algorithms applied to any choice of the input signal over any realization of the sensing matrix follows the deterministic results of the analysis closely. Simulation results are also provided which demonstrate that the proposed asymptotic analysis matches the performance of recovery algorithms for large but finite values of n . Compared to the existing technique for the analysis of NB-VB algorithms, which is based on numerically solving a large system of coupled differential equations, the proposed method is more accurate and simpler to implement.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2206368