Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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
compressive 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 $\ell$ in
the asymptotic regime where $n \rightarrow \infty$. 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 non-trivial
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 $\ell$. 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 much simpler and more accurate.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an