Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics.
We propose deterministic sampling strategies for compressive imaging based on Delsarte-Goethals frames. We show that these sampling strategies result in multi-scale measurements which can be related to the 2D Haar wavelet transform. We demonstrate the effectiveness of our proposed strategies through numerical experiments.
We propose a joint source-channel-network coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of sources within an allowed distortion level at each receiver. We perform joint source-channel coding at each source by randomly projecting source values to a lower dimensional space. We consider sources that satisfy the restricted eigenvalue (RE) condition as well as more general sources for which the randomn…
In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide an explicit trade-off between the rate and the decoding complexity. The key difference of compressive sensing and traditional information theoretic approaches is at their decoding side. Although optimal decoders to recover the original signal, compressed by source coding have high complexity, the compressive sensing decoder is a linear or convex optimizatio…
Differential pulse-code modulation (DPCM) is recently coupled with uniform scalar quantization (SQ) to improve the rate-distortion (RD) performance for the block-based quantized compressive sensing (CS) of images. In this framework, for each block's CS measurements, a prediction is generated based on the reconstructed CS measurements of the previous blocks and subtracted from measurements of the current block in the measurement domain. The resulting residual is then quantized by uniform SQ to generate the quantization index. However, the entropy coding is still required to remove the statistic…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems. Such an expression was addressed previously either by bounds, by simulations and by the (non-rigorous) replica method. The expression of the mutual information is based on techniques used in [1], addressing the minimum mean square error (MMSE) analysis. Using these expressions, we study specifically a variety of sparse linear communications models which include…
We consider compressive sensing as a source coding method for signal transmission. We concatenate a convolutional coding system with 1-bit compressive sensing to obtain a serial concatenated system model for sparse signal transmission over an AWGN channel. The proposed source/channel decoder, which we refer to as turbo CS, is robust against channel noise and its signal reconstruction performance at the receiver increases considerably through iterations. We show 12 dB improvement with six turbo CS iterations compared to a non-iterative concatenated source/channel decoder.
This article introduces a novel communication paradigm for the unsourced, uncoordinated Gaussian multiple access problem. The major components of the envisioned framework are as follows. The encoded bits of every message are partitioned into two groups. The first portion is transmitted using a compressive sensing scheme, whereas the second set of bits is conveyed using a multi-user coding scheme. The compressive sensing portion is key in sidestepping some of the challenges posed by the unsourced aspect of the problem. The information afforded by the compressive sensing is employed to create a …
This paper derives fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry …
In this paper, a compressive sensing (CS) approach is proposed for sparse binary signals' compression and reconstruction based on analog fountain codes (AFCs). In the proposed scheme, referred to as the analog fountain compressive sensing (AFCS), each measurement is generated from a linear combination of L randomly selected binary signal elements with real weight coefficients. The weight coefficients are chosen from a finite weight set and L, called measurement degree, is obtained based on a predefined degree distribution function. We propose a simple verification based reconstruction algorith…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is established when the reconstruction is also required to be sparse. The result holds in general when the distortion constraint is on the expected $p$-norm of error between the source and the reconstruction. A new restricted isometry like property is introduced for this purpose and the existence of matrices that satisfy this property is shown.
A new video coding method based on compressive sampling is proposed. In this method, a video is coded using compressive measurements on video cubes. Video reconstruction is performed by minimization of total variation (TV) of the pixelwise DCT coefficients along the temporal direction. A new reconstruction algorithm is developed from TVAL3, an efficient TV minimization algorithm based on the alternating minimization and augmented Lagrangian methods. Video coding with this method is inherently scalable, and has applications in mobile broadcast.
It is of paramount importance to achieve efficient data collection in the Internet of Things (IoT). Due to the inherent structural properties (e.g., sparsity) existing in many signals of interest, compressive sensing (CS) technology has been extensively used for data collection in IoT to improve both accuracy and energy efficiency. Apart from the existing works which leverage CS as a channel coding scheme to deal with data loss during transmission, some recent results have started to employ CS as a source coding strategy. The frequently used projection matrices in these CS-based source coding …
This paper derives fundamental limits on the performance of compressive classification when the source is a mixture of Gaussians. It provides an asymptotic analysis of a Bhattacharya based upper bound on the misclassification probability for the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity-order and coding gain in multi-antenna communications. The diversity-order of the measurement system determines the rate at which the probability of misclassification decays with signal-to-noise ratio (SNR) in the low-noise regime. The co…
Structurally random matrices (SRMs) are a practical alternative to fully random matrices (FRMs) when generating compressive sensing measurements because of their computational efficiency and their universality with respect to the sparsifing basis. In this work we derive the statistical distribution of compressive measurements generated by various types of SRMs, as a function of the signal properties. We show that under a wide range of conditions, that distribution is a mixture of asymptotically multi-variate normal components. We point out the implications for quantization and coding of the me…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random spatial patterns that are selected from an appropriate random ensemble. We show here that CS can be exploited in `native' optics hardware without introducing added components. Specifically, we show that random sub-Nyquist sampling of an interferogram helps reconstruct the field modal structure. The distribution of reduced sensing matrices corresponding to r…
This article introduces a novel paradigm for the unsourced multiple-access communication problem. This divide-and-conquer approach leverages recent advances in compressive sensing and forward error correction to produce a computationally efficient algorithm. Within the proposed framework, every active device first partitions its data into several sub-blocks, and subsequently adds redundancy using a systematic linear block code. Compressive sensing techniques are then employed to recover sub-blocks, and the original messages are obtained by connecting pieces together using a low-complexity tree…
The compressed sensing paradigm allows to efficiently represent sparse signals by means of their linear measurements. However, the problem of transmitting these measurements to a receiver over a channel potentially prone to packet losses has received little attention so far. In this paper, we propose novel methods to generate multiple descriptions from compressed sensing measurements to increase the robustness over unreliable channels. In particular, we exploit the democracy property of compressive measurements to generate descriptions in a simple manner by partitioning the measurement vector …
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 re…
Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for distributed compressive sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. Our theoretical contribution is to characterize the fundamental performance limits of DCS reco…
Quantized compressive sensing (QCS) deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model. While the resolution of this quantization clearly impacts the quality of signal reconstruction, there actually exist incompatible combinations of quantization functions and sensing matrices that proscribe arbitrarily low reconstruction error when the number of measurements increases. This work shows that a large class of random matrix constructions known to res…
We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of the $K$ non-zero signal components using only slightly more than $4K$ measurements when the support of the signal is uniformly random, with order-optimal time and memory complexity of $Θ(K)$. It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is $4K - o(K)$ to recover the signal exactly and with no assu…
Recently, it was observed that spatially-coupled LDPC code ensembles approach the Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The fundamental reason for this was attributed to a "threshold saturation" phenomena derived by Kudekar, Richardson and Urbanke. In particular, it was shown that the belief propagation (BP) threshold of the spatially coupled codes is equal to the maximum a posteriori (MAP) decoding threshold of the underlying constituent codes. In this sense, the BP threshold is saturated to its maximum value. Moreover, it has been empirically obser…
Massive machine-type communications (mMTC) are poised to provide ubiquitous connectivity for billions of Internet-of-Things (IoT) devices. However, the required low-latency massive access necessitates a paradigm shift in the design of random access schemes, which invokes a need of efficient joint activity and data detection (JADD) algorithms. By exploiting the feature of sporadic traffic in massive access, a beacon-aided slotted grant-free massive access solution is proposed. Specifically, we spread the uplink access signals in multiple subcarriers with pre-equalization processing and formulat…
Spectrum resources management of growing demands is a challenging problem and Cognitive Radio (CR) known to be capable of improving the spectrum utilization. Recently, Power Spectral Density (PSD) map is defined to enable the CR to reuse the frequency resources regarding to the area. For this reason, the sensed PSDs are collected by the distributed sensors in the area and fused by a Fusion Center (FC). But, for a given zone, the sensed PSDs by neighbor CR sensors may contain a shared common component for a while. This component can be exploited in the theory of the Distributed Source Coding (D…
We put forward a new algorithmic solution to the massive unsourced random access (URA) problem, by leveraging the rich spatial dimensionality offered by large-scale antenna arrays. This paper makes an observation that spatial signature is key to URA in massive connectivity setups. The proposed scheme relies on a slotted transmission framework but eliminates the need for concatenated coding that was introduced in the context of the coupled compressive sensing (CCS) paradigm. Indeed, all existing works on CCS-based URA rely on an inner/outer tree-based encoder/decoder to stitch the slot-wise rec…
As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich colle…
Inspired by compressive sensing principles, we propose novel error control coding techniques for communication systems. The information bits are encoded in the support and the non-zero entries of a sparse signal. By selecting a dictionary matrix with suitable dimensions, the codeword for transmission is obtained by multiplying the dictionary matrix with the sparse signal. Specifically, the codewords are obtained from the sparse linear combinations of the columns of the dictionary matrix. At the decoder, we employ variations of greedy sparse signal recovery algorithms. Using Gold code sequences…
This paper advocates the use of the distributed compressed sensing (DCS) paradigm to deploy energy harvesting (EH) Internet of Thing (IoT) devices for energy self-sustainability. We consider networks with signal/energy models that capture the fact that both the collected signals and the harvested energy of different devices can exhibit correlation. We provide theoretical analysis on the performance of both the classical compressive sensing (CS) approach and the proposed distributed CS (DCS)-based approach to data acquisition for EH IoT. Moreover, we perform an in-depth comparison of the propos…
