Formulating Binary Compressive Sensing Decoding with Asymmetrical Property

Liu, Xiao Lin; Luo, Chong; Wu, Feng

doi:10.1109/dcc.2011.28

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…Restricting the vector x in the problem (1) to take its values from {0, 1} leads to an NP-hard discrete optimization problem -called binary compressive sensing (Nakarmi and Rahnavard [2012], Liu et al [2011]). From an application point of view, not only binary signal sources have real-world applications (i.e., event detection in wireless sensor networks, group testing, spectrum hole detection for cognitive radios, etc.…”

Section: Proof Of Conceptmentioning

confidence: 99%

“…While most of the studies in compressive sensing focus on random design matrices with Gaussian distribution, solid theoretical and experimental results are available to guarantee that we can also exactly recover sparse (or compressible) signals from random binary matrices with a very high probability (Zhang et al [2010]). In the realm of binary compressive sensing, however, binary coding matrices have demonstrated remarkably lower performance compared to non-binary design matrices (Nakarmi and Rahnavard [2012], Liu et al [2011]). As an illustration, sparse random design matrices with Bernoulli distribution can only recover highly sparse binary signals -s/N < 0.1 (RefBCS).…”

Section: Proof Of Conceptmentioning

confidence: 99%

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SAT-based Compressive Sensing

Ayanzadeh,

Halem,

Finin

2019

Preprint

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We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate. The original problem of compressive sensing in sparse recovery is NP-hard; therefore, in addition to restrictions for the uniqueness of the sparse solution, the coding matrix has also to satisfy additional stringent constraints-usually the restricted isometry property (RIP)-so we can handle it by its convex or nonconvex relaxations. In practice, such constraints are not only intractable to be verified but also invalid in broad applications. This paper bridges the gap between employing modern SAT solvers and a vast variety of compressive sensing based real-world applications. We first divide the wellposed problem of compressive sensing into relaxed sub-problems and represent them as separate SAT instances in conjunctive normal form (CNF). After merging the resulting sub-problems, we assign weights to all clauses in such a way that the aggregated weighted-MAX-SAT can guarantee successful recovery of the original signal. The only requirement in our approach is the solution uniqueness of the associated problems, which is notably looser. As a proof of concept, we demonstrate the applicability of our approach in tackling the original problem of binary compressive sensing with binary design matrices. Experimental results demonstrate the supremacy of the proposed SAT-based compressive sensing over the 1 -minimization in the robust recovery of sparse binary signals. SAT-based compressive sensing on average requires 8.3% fewer measurements for exact recovery of highly sparse binary signals (s/N ≈ 0.1). When s/N ≈ 0.5, the 1 -minimization on average requires 22.2% more measurements for exact reconstruction of the binary signals. Thus, the proposed SAT-based compressive sensing is less sensitive to the sparsity of the original signals.Preprint. Under review.

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Section: Proof Of Conceptmentioning

confidence: 99%

Section: Proof Of Conceptmentioning

confidence: 99%

SAT-based Compressive Sensing

Ayanzadeh,

Halem,

Finin

2019

Preprint

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“…Wu et al [39] characterize the CS decoding process by a set of differential equations and derive its closed-form formulation. Liu et al [40] improve the formulation by leveraging the asymmetrical property on decoding of bits "1" and "0." However, these works all assume erasure channels (i.e., a measurement is either correctly received or completely lost) and decoding in noisy channels (i.e., measurements are contaminated with noise) is not discussed.…”

Section: B Compressive Sensingmentioning

confidence: 99%

Fast Decoding and Hardware Design for Binary-Input Compressive Sensing

Wang

Shi

et al. 2012

IEEE J. Emerg. Sel. Topics Circuits Syst.

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Binary-input compressive sensing (BiCS) has recently been applied to wireless communications as a modulated coding scheme for seamless rate adaptation. Different from conventional channel codes which generate binary symbols with logical-OR (XOR) operations, BiCS generates multilevel symbols through weighted sum operation. Although BiCS can be decoded by message passing, it needs to compute the convolution of probability functions in each iteration. The high decoding complexity has prevented the technique from being applied to practical use. In this paper, we propose a fast BiCS decoding algorithm and its corresponding partial-parallel hardware design. In this algorithm, we first build lookup tables to solve the computationally intensive problem of convolution. Through these tables, we successfully convert the convolution of probabilities into the polynomial of some exponential terms. This key step allows us to use log-likelihood ratio as message in message passing decoding and a fast algorithm is developed by approximate computing. We further design a partial-parallel hardware decoder. To avoid memory collision, we propose a multilevel cyclic-shift approach to generate the CS measurement matrix. We design horizontal unit processors with the proposed tables for iterative computing. Our analyses show that the proposed fast algorithm can reduce multiplications by nearly 90%. The decoding speed of our field-programmable gate array design reaches the range of communication rate in modern wireless networks.Index Terms-Compressive sensing (CS), fast decoding, message passing, random projection codes, wireless rate adaptation.

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Compressive Coded Modulation for Seamless Rate Adaptation

Cui

Luo

et al. 2013

IEEE Trans. Wireless Commun.

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Formulating Binary Compressive Sensing Decoding with Asymmetrical Property

Cited by 5 publications

References 14 publications

SAT-based Compressive Sensing

SAT-based Compressive Sensing

Fast Decoding and Hardware Design for Binary-Input Compressive Sensing

Compressive Coded Modulation for Seamless Rate Adaptation

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