Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes
TLDR
In this article, the behavior of approximate message-passing (AMP), a solver for linear sparse estimation problems such as compressed sensing, when the i.i.d matrices, for which it has been specifically designed, are replaced by structured operators, such as Fourier and Hadamard ones, was investigated.Abstract:
We study the behavior of approximate message-passing (AMP), a solver for linear sparse estimation problems such as compressed sensing, when the i.i.d matrices—for which it has been specifically designed—are replaced by structured operators, such as Fourier and Hadamard ones. We show empirically that after proper randomization, the structure of the operators does not significantly affect the performances of the solver. Furthermore, for some specially designed spatially coupled operators, this allows a computationally fast and memory efficient reconstruction in compressed sensing up to the information-theoretical limit. We also show how this approach can be applied to sparse superposition codes, allowing the AMP decoder to perform at large rates for moderate block length.read more
Citations
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Statistical physics of inference: thresholds and algorithms
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TL;DR: The connection between inference and statistical physics is currently witnessing an impressive renaissance and the current state-of-the-art is reviewed, with a pedagogical focus on the Ising model which, formulated as an inference problem, is called the planted spin glass.
Journal ArticleDOI
Statistical physics of inference: Thresholds and algorithms
Lenka Zdeborová,Florent Krzakala +1 more
TL;DR: In this paper, the authors provide a pedagogical review of the current state-of-the-art algorithms for the planted spin glass problem, with a focus on the Ising model.
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Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes
Jean Barbier,Florent Krzakala +1 more
TL;DR: In this article, the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel was studied and two solutions to reach the Shannon capacity were proposed: 1) a power allocation strategy and 2) spatial coupling.
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Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
TL;DR: In this article, the authors consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections and show that approximate message-passing always reaches the minimal-mean-square error.
Journal ArticleDOI
Approximate message-passing decoder and capacity-achieving sparse superposition codes
Jean Barbier,Florent Krzakala +1 more
TL;DR: Simulations suggest that spatial coupling is more robust and allows for better reconstruction at finite code lengths, and it is shown empirically that the use of a fast Hadamard-based operator allows for an efficient reconstruction, both in terms of computational time and memory, and the ability to deal with very large messages.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
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Single-Pixel Imaging via Compressive Sampling
Marco F. Duarte,Mark A. Davenport,Dharmpal Takhar,Jason N. Laska,Ting Sun,Kevin F. Kelly,Richard G. Baraniuk +6 more
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Message-passing algorithms for compressed sensing
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Analytic and Algorithmic Solution of Random Satisfiability Problems
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