The Shannon lower bound has been the subject of several important contributions by Berger. This paper surveys Shannon bounds on rate-distortion problems under mean-squared error distortion with a particular emphasis o...
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The Shannon lower bound has been the subject of several important contributions by Berger. This paper surveys Shannon bounds on rate-distortion problems under mean-squared error distortion with a particular emphasis on Berger's techniques. Moreover, as a new result, the Gray-Wyner network is added to the canon of settings for which such bounds are known. In the Shannon bounding technique, elegant lower bounds are expressed in terms of the source entropy power. Moreover, there is often a complementary upper bound that involves the source variance in such a way that the bounds coincide in the special case of Gaussian statistics. Such pairs of bounds are sometimes referred to as Shannon bounds. The present paper puts Berger's work on many aspects of this problem in the context of more recent developments, encompassing indirect and remote source coding such as the CEO problem, originally proposed by Berger, as well as the Gray-Wyner network as a new contribution.
Binaural hearing aids (HAs) can potentially perform advanced noise reduction algorithms, leading to an improvement over monaural/bilateral HAs. Due to the limited transmission capacities between the HAs and given know...
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Binaural hearing aids (HAs) can potentially perform advanced noise reduction algorithms, leading to an improvement over monaural/bilateral HAs. Due to the limited transmission capacities between the HAs and given knowledge of the complete joint noise signal statistics, the optimal rate-constrained beamforming strategy is known from the literature. However, as these joint statistics are unknown in practice, sub-optimal strategies have been presented. In this paper, we present a unified framework to study the performance of these existing optimal and sub-optimal rate-constrained beamforming methods for binaural HAs. Moreover, we propose to use an asymmetric sequential coding scheme to estimate the joint statistics between the microphones in the two HAs. We show that under certain assumptions, this leads to suboptimal performance in one HA but allows to obtain the truly optimal performance in the second HA. Based on the mean square error distortion measure, we evaluate the performance improvement between monaural beamforming (no communication) and the proposed scheme, as well as the optimal and the existing sub-optimal strategies in terms of the information hit-rate. The results show that the proposed method outperforms existing practical approaches in most scenarios, especially at middle rates and high rates, without having the prior knowledge of the joint statistics.
We consider the recovery of a continuous-time Wiener process from a quantized or a lossy compressed version of its uniform samples under limited bitrate and sampling rate. We derive a closed-form expression for the op...
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We consider the recovery of a continuous-time Wiener process from a quantized or a lossy compressed version of its uniform samples under limited bitrate and sampling rate. We derive a closed-form expression for the optimal tradeoff among sampling rate, bitrate, and quadratic distortion in this setting. This expression is given in terms of a reverse waterfilling formula over the asymptotic spectral distribution of a sequence of finite-rank operators associated with the optimal estimator of the Wiener process from its samples. We show that the ratio between this expression and the standard distortion rate function of the Wiener process, describing the optimal tradeoff between bitrate and distortion without a sampling constraint, is only a function of the number of bits per sample. We also consider a sub-optimal lossy compression scheme in which the continuous-time process is estimated from the output of an encoder that is optimal with respect to the discrete-time samples. We show that the latter is strictly greater than the distortion under optimal encoding but only by at most 3%. We, therefore, conclude that near optimal performance is attained even if the encoder is unaware of the continuous-time origin of the samples.
We investigate lossy compressed sensing (CS) of a hidden, or remote, source, where a sensor observes a sparse information source indirectly. The compressed noisy measurements are communicated to the decoder for signal...
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We investigate lossy compressed sensing (CS) of a hidden, or remote, source, where a sensor observes a sparse information source indirectly. The compressed noisy measurements are communicated to the decoder for signal reconstruction with the aim to minimize the mean square error distortion. An analytically tractable lower bound to the remote rate-distortion function (RDF), i.e., the conditional remote RDF, is derived by providing support side information to the encoder and decoder. For this setup, the best encoder separates into an estimation step and a transmission step. A variant of the Blahut-Arimoto algorithm is developed to numerically approximate the remote RDF. Furthermore, a novel entropy coding based quantized CS method is proposed. Numerical results illustrate the main rate-distortion characteristics of the lossy CS, and compare the performance of practical quantized CS methods against the proposed limits.
Wireless sensor networks (WSNs) consisting of battery-powered sensors are increasingly deployed for a myriad of Internet of Things applications, e. g., environmental, industrial, and healthcare monitoring. Since wirel...
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Wireless sensor networks (WSNs) consisting of battery-powered sensors are increasingly deployed for a myriad of Internet of Things applications, e. g., environmental, industrial, and healthcare monitoring. Since wireless access is typically the main contributor to battery usage, minimizing communications is crucial to prolong network lifetime and improve user experience. The objective of this thesis is to develop and analyze energy-efficient distributed compressed data acquisition techniques for WSNs. The thesis proposes four approaches to conserve sensors energy by minimizing the amount of information each sensor has to transmit to meet given application requirements. The first part addresses a cross-layer design to minimize the sensors sum transmit power via joint optimization of resource allocation and multi-path routing. A distributed consensus optimization based algorithm is proposed to solve the problem. The algorithm is shown to have superior convergence compared to several baselines. The remaining parts deal with compressed sensing (CS) of sparse/compressible sources. The second part focuses on the distributed CS acquisition of spatially and temporally correlated sensor data streams. A CS algorithm based on sliding window and recursive decoding is developed. The method is shown to achieve higher reconstruction accuracy with fewer transmissions and less decoding delay and complexity compared to several baselines, and to progressively refine past estimates. The last two approaches incorporate the quantization of CS measurements and focus on lossy sourcecoding. The third part addresses the distributed quantized CS (QCS) acquisition of correlated sparse sources. A distortion-rate optimized variable-rate QCS method is proposed. The method is shown to achieve higher distortion-rate performance than the baselines and to enable a trade-off between compression performance and encoding complexity via the pre-quantization of measurements. The fourth part investigates
The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined sourcecoding and sub-Nyquist reconstruction problem in which the input to ...
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The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined sourcecoding and sub-Nyquist reconstruction problem in which the input to the encoder is a noisy sub-Nyquist sampled version of the analog source. We first derive an expression for the mean squared error in the reconstruction of the process from a noisy and information rate-limited version of its samples. This expression is a function of the sampling frequency and the average number of bits describing each sample. It is given as the sum of two terms: minimum mean square error in estimating the source from its noisy but otherwise fully observed sub-Nyquist samples, and a second term obtained by reverse waterfilling over an average of spectral densities associated with the polyphase components of the source. We extend this result to multi-branch uniform sampling, where the samples are available through a set of parallel channels with a uniform sampler and a pre-sampling filter in each branch. Further optimization to reduce distortion is then performed over the pre-sampling filters, and an optimal set of pre-sampling filters associated with the statistics of the input signal and the sampling frequency is found. This results in an expression for the minimal possible distortion achievable under any analog-to-digital conversion scheme involving uniform sampling and linear filtering. These results thus unify the Shannon-Whittaker-Kotelnikov sampling theorem and Shannon rate-distortion theory for Gaussian sources.
We study the problem of remote reconstruction of a continuous signal from its multiple corrupted versions. We are interested in the optimal number of samples and their locations for each corrupted signal to minimize t...
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ISBN:
(纸本)9781509045457
We study the problem of remote reconstruction of a continuous signal from its multiple corrupted versions. We are interested in the optimal number of samples and their locations for each corrupted signal to minimize the total reconstruction distortion of the remote signal. The correlation among the corrupted signals can be utilized to reduce the sampling rate. For a class of Gaussian signals, we show that in the low sampling rate region, it is optimal to use a certain nonuniform sampling scheme on all the signals. On the other hand, in the high sampling rate region, it is optimal to uniformly sample all the signals. We also show that both of these sampling strategies are optimal if we are interested in recovering the set of corrupted signals, rather than the remote signal.
We consider a multiterminal sourcecoding problem in which a source is estimated at a central processing unit from lossy-compressed remote observations. Each lossy-encoded observation is produced by a remote sensor. T...
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ISBN:
(纸本)9781509010905
We consider a multiterminal sourcecoding problem in which a source is estimated at a central processing unit from lossy-compressed remote observations. Each lossy-encoded observation is produced by a remote sensor. The sensor first obtains a noisy version of the source, then compresses this observation based on minimizing a local distortion measure that depends only on the marginal distribution of its observation. The central node, on the other hand, has knowledge of the joint distribution of the source and all the observations and produces the source estimate that minimizes a different distortion measure between the source and its reconstruction. In this paper, we investigate the problem of optimally choosing the rate of each lossy-compressed remote estimate so as to minimize the distortion at the central processor, subject to bound on the sum of the communication rate between the sensors and the central unit. We focus, in particular, on two models of practical relevance: the case of a Gaussian source observed in additive Gaussian noise and reconstructed under quadratic distortion, and the case of a binary source observed in bit-flipping noise and reconstructed under Hamming distortion. In both scenarios we show that there exist regimes under which having more remote encoders does not reduce the source distortion. In other words, having fewer, high-quality remote estimates provides a smaller distortion than having more, lower-quality estimates.
We consider a multiterminal sourcecoding problem in which a random source signal is estimated from encoded versions of multiple noisy observations. Each encoded version, however, is compressed so as to minimize a loc...
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ISBN:
(纸本)9781509018062
We consider a multiterminal sourcecoding problem in which a random source signal is estimated from encoded versions of multiple noisy observations. Each encoded version, however, is compressed so as to minimize a local distortion measure, defined only with respect to the distribution of the corresponding noisy observation. The original source is then estimated from these compressed noisy observations. We denote the minimal distortion under this coding scheme as the compress-and-estimate distortion-rate function (CE-DRF). We derive a single-letter expression for the CE-DRF in the case of an i.i.d source. We evaluate this expression for the case of a Gaussian source observed through multiple parallel AWGN channels and quadratic distortion and in the case of a non-uniform binary i.i.d source observed through multiple binary symmetric channels under Hamming distortion. For the case of a Gaussian source, we compare the performance for centralized encoding versus that of distributed encoding. In the centralized encoding scenario, when the code rates are sufficiently small, there is no loss of performance compared to the indirect sourcecoding distortionrate function, whereas distributed encoding achieves distortion strictly larger then the optimal multiterminal sourcecoding scheme. For the case of a binary source, we show that even with a single observation, the CE-DRF is strictly larger than that of indirect sourcecoding.
The problem of transmitting a remotesource via multiple agents to a single destination is considered with secrecy constraints. In particular, noisy versions of a source are observed by multiple agents who then encode...
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ISBN:
(纸本)9781479970889
The problem of transmitting a remotesource via multiple agents to a single destination is considered with secrecy constraints. In particular, noisy versions of a source are observed by multiple agents who then encode and transmit their observations to a decoder over dedicated noisy channel. The decoder should be able to reconstruct the remotesource within a certain distortion limit. In addition, there exists an eavesdropper with correlated side information to the source who is capable of wiretapping the links from the agents to the decoder so as to extract as much information as possible about the source. Therefore, the agents should encode their observations in such a way that while as less information as possible is leaked to the eavesdropper the decoder can satisfy the distortion constraint. For this problem, we study the tradeoffs among agents' transmission rates, experienced distortion at the destination, and equivocation rates at the eavesdropper, and provide an achievable region.
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