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Asymmetric coding for Rate-Constrained Noise Reduction in Binaural Hearing Aids

IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2019年第1期27卷 154-167页

作者： Amini, Jamal Hendriks, Richard C. Heusdens, Richard Guo, Meng Jensen, Jesper Delft Univ Technol Dept Elec Engn Math & Comp Engn NL-2628 CD Delft Netherlands Oticon AS DK-2765 Smorum Denmark Aalborg Univ Elect Syst Dept DK-9100 Aalborg Denmark

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.

关键词： Binaural hearing aids (HAs) multi-microphone noise reduction remote source coding

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On the Optimal Performance in Asymmetric Gaussian Wireless Sensor Networks With Fading

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第4期58卷 2436-2441页

作者： Behroozi, Hamid Alajaji, Fady Linder, Tamas Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada

We study the estimation of a Gaussian source by a Gaussian wireless sensor network (WSN) where distributed sensors transmit noisy observations of the source through a fading Gaussian multiple access channel to a fusion center. In a recent work Gastpar, ["Uncoded transmission is exactly optimal for a Simple Gaussian Sensor Network," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 5247-5251, Nov. 2008] showed that for a symmetric Gaussian WSN with no fading, uncoded (analog) transmission achieves the optimal performance theoretically attainable (OPTA). In this correspondence, we consider an asymmetric fading WSN in which the sensors have differing noise and transmission powers. We first present lower and upper bounds on the system's OPTA under random fading. We next focus on asymmetric networks with deterministic fading. By comparing the obtained lower and upper OPTA bounds under deterministic fading, we provide a sufficient condition for the optimality of the uncoded transmission scheme for a given power tuple P = (P-1, P-2, ... , P-L). Then, allowing the sensor powers to vary under a weighted sum constraint (this includes the sum-power constraint as a special case), we obtain a sufficient condition for the optimality of uncoded transmission and provide the system's corresponding OPTA.

关键词： Gaussian multiple access channel with fading joint source-channel coding power-distortion tradeoff remote source coding sensor networks uncoded transmission

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Distortion Rate Function of Sub-Nyquist Sampled Gaussian sources

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第1期62卷 401-429页

作者： Kipnis, Alon Goldsmith, Andrea J. Eldar, Yonina C. Weissman, Tsachy Stanford Univ Dept Elect Engn Stanford CA 94305 USA Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined source coding 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.

关键词： source coding rate-distortion sub-Nyquist sampling remote source coding Gaussian processes

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Rate-Distortion Performance of Lossy Compressed Sensing of Sparse sources

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IEEE TRANSACTIONS ON COMMUNICATIONS 2018年第10期66卷 4498-4512页

作者： Leinonen, Markus Codreanu, Marian Juntti, Markku Kramer, Gerhard Univ Oulu Ctr Wireless Commun Radio Technol Oulu 90014 Finland Tech Univ Munich Inst Commun Engn D-80290 Munich Germany

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.

关键词： remote source coding conditional rate-distortion theory side information Blahut-Arimoto algorithm wireless sensor networks

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Shannon Bounds for Quadratic Rate-Distortion Problems

IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY

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IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY 2024年 5卷 597-608页

作者： Gastpar, Michael Sula, Erixhen Ecole Polytech Fed Lausanne Sch Comp & Commun Sci CH-1015 Lausanne Switzerland MIT Dept Elect Engn & Comp Sci 77 Massachusetts Ave Cambridge MA 02139 USA

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.

关键词： Rate-distortion Shannon lower bound conditional rate-distortion Wyner-Ziv rate-distortion function remote source coding indirect source coding Gray-Wyner network CEO problem

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The Distortion-Rate Function of Sampled Wiener Processes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第1期65卷 482-499页

作者： Kipnis, Alon Goldsmith, Andrea J. Eldar, Yonina C. Stanford Univ Dept Stat Stanford CA 94305 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

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.

关键词： Brownian motion Wiener process sampling remote source coding lossy compression analog to digital conversion compress and estimate Brownian bridge

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SAMPLING AND DISTORTION TRADEOFFS FOR INDIRECT source RETRIEVAL

SAMPLING AND DISTORTION TRADEOFFS FOR INDIRECT SOURCE RETRIE...

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IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Mohammadi, Elaheh Fallah, Alireza Marvasti, Farokh Sharif Univ Technol Dept Elect Engn Adv Commun Res Inst ACRI Tehran Iran

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.

关键词： remote source coding Distortion Non-uniform Sampling

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On Transmission of a remote source With Secrecy Constraints Over Noisy Channels

On Transmission of a Remote Source With Secrecy Constraints ...

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IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Naghibi, Farshad Salimi, Somayeh Skoglund, Mikael KTH Royal Inst Technol Sch Elect Engn SE-10044 Stockholm Sweden KTH Royal Inst Technol ACCESS Linnaeus Ctr SE-10044 Stockholm Sweden

ISBN: (纸本)9781479970889

The problem of transmitting a remote source 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 remote source 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.

关键词： remote source coding CEO problem secrecy constraints eavesdropping

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Optimal Rate Allocation in Multiterminal Compress-and-Estimate source coding

Optimal Rate Allocation in Multiterminal Compress-and-Estima...

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IEEE Information Theory Workshop (ITW)

作者： Song, Ruiyang Rini, Stefano Kipnis, Alon Goldsmith, Andrea J. Tsinghua Univ Beijing Peoples R China Natl Chiao Tung Univ Hsinchu Taiwan Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9781509010905

We consider a multiterminal source coding 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.

关键词： remote source coding Binary source Gaussian source Binary symmetric channel CEO problem

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High-resolution source coding for non-difference distortion measures: The rate-distortion function

High-resolution source coding for non-difference distortion ...

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ISIT 97 Meeting

作者： Linder, T Zamir, R Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada Tel Aviv Univ Dept Elect Engn Syst IL-69978 Ramat Aviv Israel

ISBN: (纸本)0780339568

The problem of asymptotic (i.e., low-distortion) behavior of the rate distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x, y) = parallel to W(x)(Y - x)parallel to(2), y, x is an element of R-n, the asymptotic expression for the rate-distortion function of X is an element of R-n at distortion level D equals h(X) - n/2 log (2 pi eD/n) + E log \det W(X)\ where h(X) is the differential entropy of X. Extensions to staionary sources and to high-resolution remote ("noisy") source coding are also given. In a companion paper in this issue these results are applied to develop a high-resolution quantization theory for non-difference distortion measures.

关键词： asymptotic quantization theory Shannon lower bound non-difference distortion measures rate-distortion function remote source coding

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