The data acquired at different scalp EEG electrodes when human subjects are exposed to speech stimuli are highly redundant. The redundancy is partly due to volume conduction effects and partly due to localized regions of the brain synchronizing their activity in response to the stimuli. In a competing talker scenario, we use a recent measure of directed redundancy to assess the amount of redundant information that is causally conveyed from the attended stimuli to the left temporal region of the brain. We observe that for the attended stimuli, the transfer entropy as well as the directed redundancy is proportional to the correlation between the speech stimuli and the reconstructed signal from the EEG signals. This demonstrates that both the rate as well as the rate-redundancy are inversely proportional to the distortion in neural speech tracking. Thus, a greater rate indicates a greater redundancy between the electrode signals, and a greater correlation between the reconstructed signal and the attended stimuli. A similar relationship is not observed for the distracting stimuli.

Hearing aid (HA) users often experience increased listening effort, particularly in noisy environments. While noise reduction (NR) algorithms aim to alleviate this, traditional electroencephalography (EEG) methods based on power analysis have limited success in assessing the listening effort in this population. This study proposes a novel method using a whole-head synchronization map analysis that uses local connectivity, a measure of statistical dependencies within localized brain regions. We use EEG electrodes to define a region based on the surrounding electrodes in the first-order neighborhood. This approach was tested using EEG data from 22 HA users with active or inactive NR engaged in a continuous speech-in-noise (SiN) task at low (3dB) and high (8dB) signal-to-noise ratio (SNR) levels. Whole-head synchronization was quantified using circular omega complexity (COC), a multivariate phase synchrony measure. Results showed increased local connectivity in the alpha band (8–12 Hz) within frontal and occipital regions during SiN condition compared to the background noise-only (NO) condition. Furthermore, NR activation impacted the synchronization map differently at the two SNRs of the experiment, with greater effect observed at low SNR, primarily in the left parietal region and alpha band. This behavior is in line with that of existing measures for listening effort, and therefore suggests that EEG local connectivity analysis holds promise as a tool for objectively assessing listening effort in HA users, especially in challenging listening environments.

While attention-based architectures, such as Conformers, excel in speech enhancement, they face challenges such as scalability with respect to input sequence length. In contrast, the recently proposed Extended Long Short-Term Memory (xLSTM) architecture offers linear scalability. However, xLSTM-based models remain unexplored for speech enhancement. This paper introduces xLSTM-SENet, the first xLSTM-based single-channel speech enhancement system. A direct comparative analysis reveals that xLSTM-and notably, even LSTM-can match or outperform state-of-the-art Mamba- and Conformer-based systems across various model sizes in speech enhancement on the VoiceBank+Demand dataset. Through ablation studies, we identify key architectural design choices such as exponential gating and bidirectionality contributing to its effectiveness. Our best xLSTM-based model, xLSTM-SENet2, outperforms state-of-the-art Mamba- and Conformer-based systems of similar complexity on the Voicebank+DEMAND dataset.

This paper addresses the problem of near-end listening enhancement (NELE), where a clean speech signal is modified prior to playback and under an energy constraint to improve intelligibility in noise. We analyze a recently proposed NELE method, optimized using a Speech Intelligibility Index that has been modified to incorporate temporal aspects of the noise via long-term fractile noise statistics. Specifically, we explain the energy allocation strategy adopted by the algorithm, and show that, in contrast to many existing methods, the spectral energy distribution of the modified speech is a function of that of the background noise, but not that of the input speech. Our simulation experiments show that this simple method outperforms well-established spectral shaping NELE methods. In addition, we extend the algorithm by appending an off-the-shelf dynamic range compressor, and show that it performs generally better than state-of-the-art methods for NELE.

In this paper, we propose the use of self-supervised pretraining on a large unlabelled data set to improve the performance of a personalized voice activity detection (VAD) model in adverse conditions. We pretrain a long short-term memory (LSTM)-encoder using the autoregressive predictive coding (APC) framework and fine-tune it for personalized VAD. We also propose a denoising variant of APC, with the goal of improving the robustness of personalized VAD. The trained models are systematically evaluated on both clean speech and speech contaminated by various types of noise at different SNR-levels and compared to a purely supervised model. Our experiments show that self-supervised pretraining not only improves performance in clean conditions, but also yields models which are more robust to adverse conditions compared to purely supervised learning.

Diffusion models are a new class of generative models that have recently been applied to speech enhancement successfully. Previous works have demonstrated their superior performance in mismatched conditions compared to state-of-the art discriminative models. However, this was investigated with a single database for training and another one for testing, which makes the results highly dependent on the particular databases. Moreover, recent developments from the image generation literature remain largely unexplored for speech enhancement. These include several design aspects of diffusion models, such as the noise schedule or the reverse sampler. In this work, we systematically assess the generalization performance of a diffusion-based speech enhancement model by using multiple speech, noise and binaural room impulse response (BRIR) databases to simulate mismatched acoustic conditions. We also experiment with a noise schedule and a sampler that have not been applied to speech enhancement before. We show that the proposed system substantially benefits from using multiple databases for training, and achieves superior performance compared to state-of-the-art discriminative models in both matched and mismatched conditions. We also show that a Heun-based sampler achieves superior performance at a smaller computational cost compared to a sampler commonly used for speech enhancement.

Speech enhancement in hearing aids (HAs) can take advantage of a wireless remote microphone (RM) having a better signal-to-noise ratio than the HA microphones. However, using the RM effectively is complicated by the time delay between the acoustic and wireless signals. Methods in the literature assume an instantaneous transmission of the RM signal, which is never the case in practice. Hence, we propose a practically operational method to use an RM with HAs in the presence of wireless transmission delays. Specifically, we use the delayed target voice activity state from the RM signal, to derive an expression for target speech presence probability (SPP) at the local HA microphone signals. The proposed method uses this target SPP mask as a post-filter that follows a local multichannel Wiener filter. Through simulations, we demonstrate that the proposed method improves speech quality and intelligibility metrics, especially in very noisy acoustic environments, compared to a standard approach which relies solely on HA microphones.

We quantify the average amount of redundant information that is transferred from a subset of relevant random source processes to a target process. To identify the relevant source processes, we consider those that are connected to the target process and in addition share a certain proportion of the total information causally provided to the target. Even if the rel-evant processes have no directed information exchange between them, they can still causally provide redundant information to the target. This makes it difficult to identify the relevant processes. To solve this issue, we propose the existence of a hidden redundancy process that governs the shared information among the relevant processes. We bound the redundancy by the minimal average directed redundancy from the relevant processes to the target, from the hidden redundancy process to the target, and from the hidden redundancy process to the relevant processes.

The proliferation of edge-based wireless speech applications necessitates the development of resource-efficient, low-latency speech communication systems capable of functioning across diverse communication channel conditions. Ensuring intelligible speech communication under conditions of constrained resources and low-latency presents a challenging problem within the domain of speech transmission. In this paper, we introduce a very low-latency configurable speech transmission system leveraging joint source-channel coding and deep neural networks (DNNs). Our proposed system is a unified deep neural network system engineered to operate effectively across a wide range of wireless communication channel scenarios. The system encompasses both a joint source-channel encoder and a joint source-channel decoder, each with access to channel state information (CSI). In this context, CSI signifies the type of fading in the wireless channel. Notably, our system has a total latency of 2 ms. Through extensive simulations, we empirically demonstrate that the proposed configurable system closely approximates the performance of ideal systems specifically tailored to individual wireless channel scenarios. Our evaluation is rooted in the assessment of instrumental measures of speech quality and intelligibility, affirming the efficacy of our system in diverse and resource-constrained communication contexts.

The performance of deep neural network-based speech enhancement systems typically increases with the training dataset size. However, studies that investigated the effect of training dataset size on speech enhancement performance did not consider recent approaches, such as diffusion-based generative models. Diffusion models are typically trained with massive datasets for image generation tasks, but whether this is also required for speech enhancement is unknown. Moreover, studies that investigated the effect of training dataset size did not control for the data diversity. It is thus unclear whether the performance improvement was due to the increased dataset size or diversity. Therefore, we systematically investigate the effect of training dataset size on the performance of popular state-of-the-art discriminative and diffusion-based speech enhancement systems in matched conditions. We control for the data diversity by using a fixed set of speech utterances, noise segments and binaural room impulse responses to generate datasets of different sizes. We find that the diffusion-based systems perform the best relative to the discriminative systems in terms of objective metrics with datasets of 10 h or less. However, their objective metrics performance does not improve when increasing the training dataset size as much as the discriminative systems, and they are outperformed by the discriminative systems with datasets of 100 h or more.

Diffusion models are a new class of generative models that have shown outstanding performance in image generation literature. As a consequence, studies have attempted to apply diffusion models to other tasks, such as speech enhancement. A popular approach in adapting diffusion models to speech enhancement consists in modelling a progressive transformation between the clean and noisy speech signals. However, one popular diffusion model framework previously laid in image generation literature did not account for such a transformation towards the system input, which prevents from relating the existing diffusion-based speech enhancement systems with the aforementioned diffusion model framework. To address this, we extend this framework to account for the progressive transformation between the clean and noisy speech signals. This allows us to apply recent developments from image generation literature, and to systematically investigate design aspects of diffusion models that remain largely unexplored for speech enhancement, such as the neural network preconditioning, the training loss weighting, the stochastic differential equation (SDE), or the amount of stochasticity injected in the reverse process. We show that the performance of previous diffusion-based speech enhancement systems cannot be attributed to the progressive transformation between the clean and noisy speech signals. Moreover, we show that a proper choice of preconditioning, training loss weighting, SDE and sampler allows to outperform a popular diffusion-based speech enhancement system while using fewer sampling steps, thus reducing the computational cost by a factor of four.

Advanced auditory models are useful in designing signal-processing algorithms for hearing-loss compensation or speech enhancement. Such auditory models provide rich and detailed descriptions of the auditory pathway, and might allow for individualization of signal-processing strategies, based on physiological measurements. However, these auditory models are often computationally demanding, requiring significant time to compute. To address this issue, previous studies have explored the use of deep neural networks to emulate auditory models and reduce inference time. While these deep neural networks offer impressive efficiency gains in terms of computational time, they may suffer from uneven emulation performance as a function of auditory-model frequency-channels and input sound pressure level, making them unsuitable for many tasks. In this study, we demonstrate that the conventional machine-learning optimization objective used in existing state-of-the-art methods is the primary source of this limitation. Specifically, the optimization objective fails to account for the frequency- and level-dependencies of the auditory model, caused by a large input dynamic range and different types of hearing losses emulated by the auditory model. To overcome this limitation, we propose a new optimization objective that explicitly embeds the frequency- and level-dependencies of the auditory model. Our results show that this new optimization objective significantly improves the emulation performance of deep neural networks across relevant input sound levels and auditory-model frequency channels, without increasing the computational load during inference. Addressing these limitations is essential for advancing the application of auditory models in signal-processing tasks, ensuring their efficacy in diverse scenarios.

In the above article[1], the author characterizes the capacity of power-constrained channels with additive stationary Gaussian noise. Specifically, inSection III, the feedback capacity is shown to correspond with the solution to a variational optimization problem. Section IV gives structural properties of the solution for this optimization problem. Among these properties, it stands out the capacity-achieving optimality of using a short-length input$V$with arbitrarily small variance, and thus a power spectral density$S_{V}$equal to zero. These structural properties are further developed in its sections V and VI for first- and$m$-th-order autoregressive moving average channel noise, respectively, also showing the capacity-achieving optimality of the Schalkwijk-Kailath scheme for this scenario. In this note, we show that the proof ofCorollary 4.4in[1](which claims that the choice$S_{V} = 0$is capacity achieving) is erroneous. As a consequence, the proofs of theorems 4.1, 4.6, 5.3, and 6.1, propositions 4.7 and 5.1, as well asremarks 4.5and 5.2, and Lemma 6.1 in[1]are invalid, because they rely upon the optimality of choosing$S_{V} =0$.

We present a joint design of sound zone control filters and robust audio coding for wireless low frequency sound zones. The audio signal is filtered using sound zone control filters and encoded using a multiple-description coder. The control filters and the multiple-description coder are combined in a nested loop. The inner loop performs filtering for sound zone control and generates multiple descriptions using oversampling and closed-loop prediction. The outer loop performs noise shaping and guarantees a trade-off between robustness and quality of the descriptions. A closed-form expression for the optimal sound-zone control filters are provided, and a simulation study demonstrates that even at moderate packet loss rates, a significant gain is possible compared to not using multiple descriptions.

Distributed signal-processing algorithms in (wireless) sensor networks often aim to decentralize processing tasks to reduce communication cost and computational complexity or avoid reliance on a single device (i.e., fusion center) for processing. In this contribution, we extend a distributed adaptive algorithm for blind system identification that relies on the estimation of a stacked network-wide consensus vector at each node, the computation of which requires either broadcasting or relaying of node-specific values (i.e., local vector norms) to all other nodes. The extended algorithm employs a distributed-averaging-based scheme to estimate the network-wide consensus norm value by only using the local vector norm provided by neighboring sensor nodes. We introduce an adaptive mixing factor between instantaneous and recursive estimates of these norms for adaptivity in a time-varying system. Simulation results show that the extension provides estimation results close to the optimal fully-connected-network or broadcasting case while reducing inter-node transmission significantly.

Extracting information from fMRI data constitutes a broad active area of research. Current techniques still present several limitations; some ignore relevant aspects regarding the brain functioning or lack of interpretability. In an effort to overcome such limitations, we introduce an extension of the sparse matrix factorization approach to a multilinear decomposition. The proposed model is built upon natural justifiable assumptions and better accommodates the brain behavior. Tests on realistic synthetic as well as real fMRI datasets demonstrate significant performance gains over existing methods of this kind.

Low frequency personal sound zones can be created by controlling the sound pressure in separate spatially confined regions. The performance of a sound zone system using wireless communication may be degraded due to potential packet losses. In this paper, we propose robust FIR filters for low-frequency sound zone system by incorporating information about the expected packet losses into the design. A simulation study with eight loudspeakers surrounding two control regions shows that the proposed filters can improve the contrast and the sound quality when packet losses occur, with only a slight degradation in performance even when there is no packet loss. With the proposed filters, it is possible to gain 2 dB higher contrast on average across the frequency range 20-200Hz relative to the original filters when packet loss rate is 5%.

Current sound-based practices and systems developed in both academia and industry point to convergent research trends that bring together the field of Sound and Music Computing with that of the Internet of Things. This paper proposes a vision for the emerging field of the Internet of Sounds (IoS), which stems from such disciplines. The IoS relates to the network of Sound Things, i.e., devices capable of sensing, acquiring, processing, actuating, and exchanging data serving the purpose of communicating sound-related information. In the IoS paradigm, which merges under a unique umbrella the emerging fields of the Internet of Musical Things and the Internet of Audio Things, heterogeneous devices dedicated to musical and non-musical tasks can interact and cooperate with one another and with other things connected to the Internet to facilitate sound-based services and applications that are globally available to the users. We survey the state of the art in this space, discuss the technological and non-technological challenges ahead of us and propose a comprehensive research agenda for the field.

The intelligibility and quality of speech from a mobile phone or public announcement system are often affected by background noise in the listening environment. By pre-processing the speech signal it is possible to improve the speech intelligibility and quality — this is known as near-end listening enhancement (NLE). Although, existing NLE techniques are able to greatly increase intelligibility in harsh noise environments, in favorable noise conditions the intelligibility of speech reaches a ceiling where it cannot be further enhanced. Actually, the focus of existing methods solely on improving the intelligibility causes unnecessary processing of the speech signal and leads to speech distortions and quality degradations. In this article, we provide a new rationale for NLE, where the target speech is minimally processed in terms of a processing penalty, provided that a certain performance constraint, e.g., intelligibility, is satisfied. We present a closed-form solution for the case where the performance criterion is an intelligibility estimator based on the approximated speech intelligibility index and the processing penalty is the mean-square error between the processed and the clean speech. This produces an NLE method that adapts to changing noise conditions via a simple gain rule by limiting the processing to the minimum necessary to achieve a desired intelligibility, while at the same time focusing on quality in favorable noise situations by minimizing the amount of speech distortions. Through simulation studies, we show the proposed method attains speech quality on par or better than existing methods in both objective measurements and subjective listening tests, whilst still sustaining objective speech intelligibility performance on par with existing methods.

Transfer entropy can to a certain degree assess the direction in addition to the strength of the couplings within dynamic time series. The greater the transfer entropy, the greater the strength of the dependency between time series. In this work, we are interested in quantifying the effect that a given time series (e.g., an external stimuli) has upon the coupling strength between other time series. Towards that end, we define a directed dependency index based on the difference of two causally conditioned transfer entropies. We then provide a lower bound for the dependency index, and demonstrate on synthetic data that this lower bound can be efficiently computed.

This paper considers speech enhancement of signals picked up in one noisy environment which must be presented to a listener in another noisy environment. Recently, it has been shown that an optimal solution to this problem requires the consideration of the noise sources in both environments jointly. However, the existing optimal mutual information based method requires a complicated system model that includes natural speech variations, and relies on approximations and assumptions of the underlying signal distributions. In this paper, we propose to use a simpler signal model and optimize speech intelligibility based on the Approximated Speech Intelligibility Index (ASII). We derive a closed-form solution to the joint far- and near-end speech enhancement problem that is independent of the marginal distribution of signal coefficients, and that achieves similar performance to existing work. In addition, we do not need to model or optimize for natural speech variations.

It is well known that independent (separate) encoding of$K$correlated sources may incur some rate loss compared to joint encoding, even if the decoding is done jointly. This loss is particularly evident in the multiple descriptions problem, where it is the same source that is encoded in each description. We observe that under mild conditions about the source and distortion measure, the sum-rate of$K$separately encoded individually good descriptions tends to the rate-distortion function of the joint decoder in the limit of vanishing small coding rates of the descriptions. Moreover, we then propose to successively encode the source into$K$independent descriptions in each round in order to achieve a final distortion$D$after$M$rounds. We provide two examples – a Gaussian source with mean-squared error and an exponential source with one-sided error – for which the excess rate vanishes in the limit as the number of rounds$M$goes to infinity, for any fixed$D$and$K$. This result has an interesting interpretation for a multi-round variant of the multiple descriptions problem, where after each round the encoder gets a (block) feedback regarding which of the descriptions arrived: In the limit as the number of rounds$M$goes to infinity (i.e., many incremental rounds), the total rate of received descriptions approaches the rate-distortion function. We provide theoretical and experimental evidence showing that this phenomenon is in fact more general than in the two examples above.

It was recently shown that the combination of source prediction, two-times oversampling, and noise shaping, can be used to obtain a robust (multiple-description) audio coding framework for networks with packet loss probabilities less than 10%. Specifically, it was shown that audio signals could be encoded into two descriptions (packets), which were separately sent over a communication channel. Each description yields a desired performance by itself, and when they are combined, the performance is improved. This paper extends the previous work to an arbitrary number of descriptions (packets) by using fractional oversampling and a new decoding principle. We demonstrate that, due to source aliasing, existing MSE optimized reconstruction rules from noisy sampled data, performs poorly from a perceptual point of view. A simple reconstruction rule is proposed, that improves the PEAQ objective difference grades (ODG) by more than 2 points. The proposed audio coder enables low-delay high-quality audio streaming on networks with late packet arrivals or packet losses. With a coding delay of 2.5 ms, and a total bitrate of 300 kbps, it is demonstrated that mean PEAQ ODGs around -0.65 can be obtained for 48 kHz (mono) music (pop & rock), and packet loss probabilities of 20%.

Motivated by multiple-description source coding with feedback, it was recently proposed to encode the one-sided exponential source$X$via$K$parallel channels,$Y_{1}, \ldots, Y_{K}$, such that the error signals$X-Y_{i}, i=1, \ldots, K$, are one-sided exponential and mutually independent given$X$. Moreover, it was shown that the optimal estimator$\hat{Y}$of the source$X$with respect to the one-sided error criterion, is simply given by the maximum of the outputs, i.e.,$\hat{Y}=\max\{Y_{1},\ldots, Y_{K}\}$. In this paper, we show that the distribution of the resulting estimation error$X-\hat{Y}$, is equivalent to that of the optimum noise in the backward test-channel of the one-sided exponential source, i.e., it is one-sided exponentially distributed and statistically independent of the joint output$Y_{1}, \ldots, Y_{K}$.

Most of the well-known classic beamformers have resulted from optimization problems that minimize a cost function such as the mean-square error (MSE) between the noisy speech and a reference clean speech. The rationale behind these formulations involves a speech-versus-noise dichotomy, where anything branded as noise shall be suppressed as much as possible. While leading to simple closed-form solutions and reasonably practical beamformers, this rationale has its own limitations, for instance, when the ambient noise provides context and is therefore not entirely undesirable. In this article, we offer a new rationale, where the output of the beamformer is minimally processed with respect to a certain reference signal, as long as a given performance criterion is fulfilled. We provide a case study where the performance criterion is inspired by the Speech Intelligibility Index (SII), and the processing penalty is MSE. Regarding the reference signal, we consider two cases. In the first case, the reference signal is set to the unprocessed recording from a reference microphone, giving rise to a beamformer that limits the processing of the noisy signal to a minimum necessary for fulfilling the intelligibility requirement. For the second case, the reference signal is the output of an aggressive beamformer, yielding a beamformer that essentially eliminates the noise unless the concomitant distortion of the clean speech violates the intelligibility requirement. Through simulation studies, we demonstrate some of the benefits that each of the two cases offer in relevant contexts.

In this paper, we consider the rate-distortion problem where a source X is encoded into k parallel descriptions Y1, . . ., Yk, such that the error signals X - Yi, i = 1, . . ., k, are mutually independent given X. We show that if X is one-sided exponentially distributed, the optimal decoder (estimator) under the one-sided absolute error criterion, is simply given by the maximum of the outputs Y1, . . ., Yk. We provide a closed-form expression for the rate and distortion for any k number of parallel descriptions and for any coding rate. We furthermore show that as the coding rate per description becomes asymptotically small, encoding into k parallel descriptions and using the maximum output as the source estimate, is rate-distortion optimal.

One of the challenges with the implementation of multi-microphone noise reduction systems in practical applications lies in the need for the knowledge of the speech and noise covariance matrices. Recently, a method based on Maximum Likelihood (ML) estimation addressed this problem. Despite its relative success in practical setups, this method may suggest negative spectral components for the clean speech due to noise influences. In this paper, we suggest a new estimation technique that tackles this issue by enforcing a power constraint on the estimation problem. We compare the proposed method with the ML method both in synthetic and real-life scenarios using objective measures. The results suggest that the proposed method can improve speech quality without a loss of intelligibility.

Sound zones are generated to provide independent audio reproduction to multiple people in the same room using loudspeakers. In this article, sound zones are formulated in terms of a moving horizon framework. This framework allows the reproduction scenario to be time-varying and adapt to changes e.g. in the location of the zones or in the audio signal. The framework is tested using both simulated and measured room impulse responses from eight loudspeakers in a rectangular room. The performance is investigated using signals limited between 35-500 Hz, but the framework is not limited to a particular frequency range. The experimental results show that it is possible to gain on the order of 4 dB higher separation between the zones using the proposed framework, relative to a conventional time-invariant solution. This gain arises from knowledge about the audio content currently being reproduced in the zones, and it is obtained without deteriorating the reproduction accuracy or increasing the signal energy injected into the loudspeakers.

From the eardrum to the auditory cortex, where acoustic stimuli are decoded, there are several stages of auditory processing and transmission where information may potentially be lost. In this paper, we aim at quantifying the total information loss in the human auditory system by using information theoretic tools. To do so, we consider a speech communication model, where words are uttered and sent through a noisy channel, and then received and processed by a human listener. We define a notion of information loss that is related to the human word recognition rate. To assess the word recognition rate of humans, we conduct a closed-vocabulary intelligibility test. We derive upper and lower bounds on the information loss. Simulations reveal that the bounds are tight and we observe that the information loss in the human auditory system increases as the signal to noise ratio (SNR) decreases. Our framework also allows us to study whether humans are optimal in terms of speech perception in a noisy environment. Toward that end, we derive optimal classifiers and compare the human and machine performance in terms of information loss and word recognition rate. We observe a higher information loss and lower word recognition rate for humans compared to the optimal classifiers. In fact, depending on the SNR, the machine classifier may outperform humans by as much as 8 dB. This implies that for the speech-in-stationary-noise setup considered here, the human auditory system is suboptimal for recognizing noisy words.

We consider a fixed-rate zero-delay source coding problem where a stationary vector-valued Gauss-Markov source is compressed subject to an average mean-squared error (MSE) distortion constraint. We address the problem by considering the Gaussian nonanticipative rate distortion function (NRDF) which is a lower bound to the zero-delay Gaussian RDF. Then, we use its corresponding optimal “test-channel” to characterize the stationary Gaussian NRDF and evaluate the corresponding information rates. We show that the Gaussian NRDF can be achieved by p-parallel fixed-rate scalar uniform quantizers of finite support with dithering signal up to a multiplicative distortion factor and a constant rate penalty. We demonstrate our framework with a numerical example.

Real-time streaming of audio and video have tight constraints on the delay allowed at each step in the distribution chain. In this paper, we focus on the transport layer. That is, we investigate the effect of imposing a maximum allowable delay on the symbol loss probability for a set of rate 1/2 erasure correcting codes. We define the effective symbol loss probability to be the probability that a symbol is received too late or not at all, given some maximum allowable delay. We consider networks where the source and sink communicate via a relaying node, and that this intermediate node performs recoding. The erasure correcting code used between the source and relay need not be the same as the erasure correcting code used between the relay and sink. Moreover, on the first link, we use both a block code and on the second link we use a convolutional code. In order to do a fair comparison, we also include the case where both links use the same code type. Our results show that in order to minimize the effective symbol loss, the first link should use a triangular block code. Whereas, the second link should use a convolutional or triangular code, with little to no gain of using the former over the latter.

In this paper, we present explicit code constructions for a family of (n,k,δ) convolutional codes with optimum distance profiles. The family of convolutional codes is obtained from sets of jointly superregular matrices. For the case of finite decoder memory, we evaluate the performance of the constructed codes in terms of both symbol loss probability and symbol delay. We then present a combinatorial method to calculate the exact symbol loss probability and symbol delay for each symbol individually. We compare the symbol loss probability for two specific systematic convolutional codes for the cases where the sink has infinite or finite memory. Finally, we compare the performance of our convolutional codes with optimum distance profile and random based convolutional codes.

Ozarow's test channel for the quadratic Gaussian (QG) multiple description (MD) problem consists of two correlated AWGN channels. It is known that simply replacing the AWGN channels by quantizers with equivalent statistical properties as the channels, will generally not lead to a rate-distortion optimal realization of the MD rate-distortion function. We have previously proposed a symmetric two-channel model for the QG MD problem for the case, where the two noise terms have equal variances. We show in this paper, that by replacing the AWGN channels of this model by quantizers that are statistical equivalent to the channels, will under high-resolution assumption be rate-distortion optimal. We furthermore extend this symmetric two-channel model to the asymmetric case, and provide a simple suboptimal implementation of the channel based on scalar quantizers. Simulations are provided to show the performance of the proposed implementation.

Inspired by the DANTALE II listening test paradigm, which is used for determining the intelligibility of noisy speech, we assess the hypothesis that humans maximize the probability of correct decision when recognizing words contaminated by additive Gaussian, speech-shaped noise.We first propose a statistical Gaussian communication and classification scenario, where word models are built from short term spectra of human speech, and optimal classifiers in the sense of maximum a posteriori estimation are derived.Then, we perform a listening test, where the participants are instructed to make their best guess of words contaminated with speech-shaped Gaussian noise.Comparing the human's performance to that of the optimal classifier reveals that at high SNR, humans perform comparable to the optimal classifier.However, at low SNR, the human performance is inferior to that of the optimal classifier.This shows that, at least in this specialized task, humans are generally not able to maximize the probability of correct decision, when recognizing words.

We deal with zero-delay source coding of a vector Gaussian autoregressive (AR) source subject to an average mean squared error (MSE) fidelity criterion. Toward this end, we consider the nonanticipative rate distortion function (NRDF) which is a lower bound to the causal and zero-delay rate distortion function (RDF). We use the realization scheme with feedback proposed in [1] to model the corresponding optimal “test-channel” of the NRDF, when considering vector Gaussian AR(1) sources subject to an average MSE distortion. We give conditions on the vector Gaussian AR(1) source to ensure asymptotic stationarity of the realization scheme (bounded performance). Then, we encode the vector innovations due to Kalman filtering via lattice quantization with subtractive dither and memoryless entropy coding. This coding scheme provides a tight upper bound to the zero-delay Gaussian RDF. We extend this result to vector Gaussian AR sources of any finite order. Further, we show that for infinite dimensional vector Gaussian AR sources of any finite order, the NRDF coincides with the zero-delay RDF. Our theoretical framework is corroborated with a simulation example.

A matrix is termed superregular if all of its possible submatrices are non-singular. Superregular lower triangular Toeplitz matrices are useful for MDS convolutional codes and (sequential) network codes. In this paper, we present the explicit matrix constructions for superregular lower triangular Toeplitz matrices in GF(2p)k×k, k ≤ 5. For k > 5 we provide a greedy algorithm, which (over sufficiently large fields) is guaranteed to find a superregular lower triangular Toeplitz matrix. We introduce (product preserving) joint superregularity, and extend our explicit matrix constructions to these cases. We provide methods for deriving the exact symbol loss probability and delay for any deterministic block code. We derive the exact symbol loss probability and delay for codes using a superregular lower triangular matrix and for codes using two (product preserving) jointly superregular lower triangular matrices. We then compare these results with those obtained from both simulations and our practical implementation, and for each case we also compare with random-based codes. Furthermore, our experiments show a gain in coding throughput above 40% for superregular lower triangular Toeplitz matrices over random matrices.

Due to the distributed structure of many modern audio transmission setups, it is likely to have an observation at the receiver which is correlated with the desired source at the transmitter. This observation could be used as side information to reduce the transmission rate using distributed source coding. How to integrate distributed source coding into the perceptual audio compression procedure is thus a fundamental question. In this paper, we take a completely analytical approach to this problem, in particular to the rate-distortion trade-off and the corresponding coding schemes. We then interpret the results from an audio coding perspective. The main result is that, to upgrade a regular perceptual audio coder to a distributed coder, one needs to revise the perceptual masking curve. The revised masking curve models the availability of the side information as an extra masking effect, yielding lower rates. Interestingly, this means that at least conceptually, the distributed coding scenario could be integrated into the audio coder with minor changes, and without destructing the original coder.

Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential) network codes. In this work, we provide an explicit design for all superregular lower triangular Toeplitz matrices in GF(2p) for the case of matrices with dimensions less than or equal to 5 × 5. For higher dimensional matrices, we present a greedy algorithm that finds a solution provided the field size is sufficiently high. We also introduce the notions of jointly superregular and product preserving jointly superregular matrices, and extend our explicit constructions of superregular matrices to these cases. Jointly superregular matrices are necessary to achieve optimal decoding capabilities for the case of codes with a rate lower than 1/2, and the product preserving property is necessary for optimal decoding capabilities in network recoding.

It is well known that Shannon's rate-distortion function (RDF) in the colored quadratic Gaussian (QG) case can be parametrized via a single Lagrangian variable (the water level in the reverse water filling solution). In this paper, we show that the symmetric colored QG multiple description (MD) RDF in the case of two descriptions can be parametrized in the spectral domain via two Lagrangian variables, which control the tradeoff between the side distortion, the central distortion, and the coding rate. This spectral-domain analysis is complemented by a time-domain scheme-design approach: we show that the symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma modulation and differential pulse-code modulation. In particular, two source prediction loops, one for each description, are embedded within a common noise-shaping loop, whose parameters are explicitly found from the spectral-domain characterization.

We formulate a new problem which bridges between source coding and enhancement in wireless acoustic sensor networks. We consider a network of wireless microphones, each of which encoding its own measurement under a covariance matrix distortion constraint and sending it to a fusion center. To process the data at the center, we use a recent spatio-temporal prediction filter. We assume that a weighted sum-rate for the network is specified. The problem is to allocate optimal distortion matrices to the nodes in order to achieve a maximum output SNR at the fusion center after processing the received data, while the weighted sum-rate for the network is no more than the specified value. We formulate this problem as an optimization problem for which we derive a set of equalities imposed on the solution by studying the KKT conditions. In particular, for the special case of scalar sources with two microphones and a sum-rate constraint, we derive the distortion allocation in closed form and will show that if the given sum-rate is higher than a critical value, the stationary points from the KKT conditions lead to distortion allocations which maximize the output SNR of the filter.

In this paper, we consider the problem of remote vector Gaussian source coding for a wireless acoustic sensor network. Each node receives messages from multiple nodes in the network and decodes these messages using its own measurement of the sound field as side information. The node's measurement and the estimates of the source resulting from decoding the received messages are then jointly encoded and transmitted to a neighbouring node in the network. We show that for this distributed source coding scenario, one can encode a so-called conditional sufficient statistic of the sources instead of jointly encoding multiple sources. We focus on the case where node measurements are in form of noisy linearly mixed combinations of the sources and the acoustic channel mixing matrices are invertible. For this problem, we derive the rate-distortion function for vector Gaussian sources and under covariance distortion constraints.

In this paper, we consider a distributed remote source coding problem, where a sequence of observations of source vectors is available at the encoder. The problem is to specify the optimal rate for encoding the observations subject to a covariance matrix distortion constraint and in the presence of side information at the decoder. For this problem, we derive lower and upper bounds on the rate-distortion function (RDF) for the Gaussian case, which in general do not coincide. We then provide some cases, where the RDF can be derived exactly. We also show that previous results on specific instances of this problem can be generalized using our results. We finally show that if the distortion measure is the mean squared error, or if it is replaced by a certain mutual information constraint, the optimal rate can be derived from our main result.

This paper presents a novel framework, which enables a design of rateless codes for binary input additive white Gaussian noise (BIAWGN) channels, using the ripple-based approach known from the works for the binary erasure channel (BEC). We reveal that several aspects of the analytical results from the BEC also hold in BIAWGN channels. The presented framework is applied in a code design example, which shows promising results compared to existing work. In particular it shows a great robustness towards variations in the signal-to-noise power ratio (SNR), contrary to existing codes.

In this paper, we consider robust source coding in closed-loop systems. In particular, we consider a (possibly) unstable LTI system, which is to be stabilized via a network. The network has random delays and erasures on the data-rate limited (digital) forward channel between the encoder (controller) and the decoder (plant). The feedback channel from the decoder to the encoder is assumed noiseless. Since the forward channel is digital, we need to employ quantization. We combine two techniques to enhance the reliability of the system. First, in order to guarantee that the system remains stable during packet dropouts and delays, we transmit quantized control vectors containing current control values for the decoder as well as future predicted control values. Second, we utilize multiple description coding based on forward error correction codes to further aid in the robustness towards packet erasures. In particular, we transmit M redundant packets, which are constructed such that when receiving any J packets, the current control signal as well as J-1 future control signals can be reliably reconstructed at the decoder. We prove stability subject to quantization constraints, random dropouts, and delays by showing that the system can be cast as a Markov jump linear system.

Random binning is an efficient, yet complex, coding technique for the symmetric L-description source coding problem. We propose an alternative approach, that uses the quantized samples of a bandlimited source as “descriptions”. By the Nyquist condition, the source can be reconstructed if enough samples are received. We examine a coding scheme that combines sampling and noise-shaped quantization for a scenario in which only K <;L descriptions or all L descriptions are received. Some of the received K-sets of descriptions correspond to uniform sampling while others to non-uniform sampling. This scheme achieves the optimum rate-distortion performance for uniform-sampling K-sets, but suffers noise amplification for nonuniform-sampling K-sets. We then show that by increasing the sampling rate and adding a random-binning stage, the optimal operation point is achieved for any K-set.

In this paper, we propose a novel sequential error concealment algorithm for video and images based on sparse linear prediction. Block-based coding schemes in packet loss environments are considered. Images are modelled by means of linear prediction, and missing macroblocks are sequentially reconstructed using the available groups of pixels. The optimal predictor coefficients are computed by applying a missing data regression imputation procedure with a sparsity constraint. Moreover, an efficient procedure for the computation of these coefficients based on an exponential approximation is also proposed. Both techniques provide high-quality reconstructions and outperform the state-of-the-art algorithms both in terms of PSNR and MS-SSIM.

In this paper we propose a novel spatial error concealment algorithm for video and images based on convex optimization. Block-based coding schemes in packet loss environment are considered. Missing macro blocks are sequentially reconstructed by filling them with a weighted set of templates extracted from the available neighbourhood. Moreover, a fast approximation of the optimization method is proposed. The technique produces high quality reconstructions that outperforms the state-of-the-art algorithms both in terms of PSNR and MS-SSIM.

In this paper, we present an analytical framework for designing LT codes in additive white Gaussian noise (AWGN) channels. We show that some of analytical results from binary erasure channels (BEC) also hold in AWGN channels with slight modifications. This enables us to apply a ripple-based design approach, which until now has only been used in the BEC. LT codes designed by this way show promising performance which is near the Shannon limit even with short codewords.

In this paper feedback in LT codes is investigated. The considered type of feedback is acknowledgments, where information on which symbols have been decoded is given to the transmitter. Our analysis reveals that acknowledgments has a very low potential in LT codes with standard degree distributions. Motivated by this, we analyze the impact of acknowledgments on multi-layer LT codes. In this case, feedback proves advantageous. By using only a single feedback message, it is possible to achieve a significant performance improvement compared to traditional LT codes.

In this paper we propose a new design of LT codes, which decreases the amount of necessary overhead in comparison to existing designs. The design focuses on a parameter of the LT decoding process called the ripple size. This parameter was also a key element in the design proposed in the original work by Luby. Specifically, Luby argued that an LT code should provide a constant ripple size during decoding. In this work we show that the ripple size should decrease during decoding, in order to reduce the necessary overhead. Initially we motivate this claim by analytical results related to the redundancy within an LT code. We then propose a new design procedure, which can provide any desired achievable decreasing ripple size. The new design procedure is evaluated and compared to the current state of the art through simulations. This reveals a significant increase in performance with respect to both average overhead and error probability at any fixed overhead.

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by Rcit(D), for first-order Gauss-Markov processes. Rcit(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rcop(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rcop(D) ≤ Rcit(D) + 0.5 log2(2πe) bits/sample. In order to analyze Rcit(D) for arbitrary zero-mean Gaussian stationary sources, we introduce Rcit̅(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon Rcit̅(D), we derive three closed-form upper bounds to the additive rate loss defined as Rcit̅(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D ≤ σx2, RU(D) can be realized by an additive white Gaussian noise channel surrounded by a unique set of causal pre-, post-, and feed- back niters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal niters and is guaranteed to converge to Rcit̅(D). Finally, by establishing a connection to feedback quantization, we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves an operational rate lower than Rcit̅(D) +0.254 and Rcit̅(D) + 0.754 bits/sample, respectively. This implies that the OPTA among all zero-delay source codes, denoted by Rzdop(D), is upper bounded as Rzdop(D)cit̅(D) + 1-254 <; R(D) + 1.754 bits/sample.

The additive rate-distortion function (ARDF) was developed in order to universally bound the rate loss in the Wyner-Ziv problem, and has since then been instrumental in e.g., bounding the rate loss in successive refinements, universal quantization, and other multi-terminal source coding settings. The ARDF is defined as the minimum mutual information over an additive test channel followed by estimation. In the limit of high resolution, the ADRF coincides with the true RDF for many sources and fidelity criterions. In the other extreme, i.e., the limit of low resolutions, the behavior of the ARDF has not previously been rigorously addressed. In this work, we consider the special case of quadratic distortion and where the noise in the test channel is Gaussian distributed. We first establish a link to the I-MMSE relation of Guo et al. and use this to show that for any source the slope of the ARDF near zero rate, converges to the slope of the Gaussian RDF near zero rate. We then consider the multiplicative rate loss of the ARDF, and show that for bursty sources it may be unbounded, contrary to the additive rate loss, which is upper bounded by 1/2 bit for all sources. We finally show that unconditional incremental refinement, i.e., where each refinement is encoded independently of the other refinements, is ARDF optimal in the limit of low resolution, independently of the source distribution. Our results also reveal under which conditions linear estimation is ARDF optimal in the low rate regime.

This paper studies the tight rate-distortion bound for L-channel symmetric multiple-description coding of a scalar Gaussian source with two levels of receivers. Each of the first-level receivers obtains κ of the L descriptions (κ < L). The second-level receiver obtains all L descriptions. We find that if the central distortion (corresponding to the second-level receiver) is much smaller than the side distortion (corresponding to the first-level receivers), the product of a function of the side distortions and the central distortion is asymptotically independent of the redundancy between the descriptions. Using this property, we analyze the asymptotic behavior of a practical multiple-description lattice vector quantizer (MDLVQ). Our analysis includes the treatment of the MDLVQ system from a new geometric viewpoint, which results in an expression for the side distortions using the normalized second moment of a sphere of higher dimensionality than the quantization space. The expression of the distortion product derived from the lower bound is then applied as a criterion to assess the performance loss of the considered MDLVQ system. In principle, the efficiency of other practical MD systems can also be evaluated using the derived distortion product.

We consider linear predictive coding and noise shaping for coding and transmission of auto-regressive (AR) sources over lossy networks. We generalize an existing framework to arbitrary filter orders and propose use of fixed-lag smoothing at the decoder, in order to further reduce the impact of transmission failures. We show that fixed-lag smoothing up to a certain delay can be obtained without additional computational complexity by exploiting the state-space structure. We prove that the proposed smoothing strategy strictly improves performance under quite general conditions. Finally, we provide simulations on AR sources, and channels with correlated losses, and show that substantial improvements are possible.

The problem of the rate region of the vector Gaussian multiple description with individual and central quadratic distortion constraints is studied. We have two main contributions. First, a lower bound on the rate region is derived. The bound is obtained by lower-bounding a weighted sum rate for each supporting hyperplane of the rate region. Second, the rate region for the scenario of the scalar Gaussian source is fully characterized by showing that the lower bound is tight. The optimal weighted sum rate for each supporting hyperplane is obtained by solving a single maximization problem. This is contrary to existing results, which require solving a min-max optimization problem.

This paper concerns multi path video streaming using adaptive multiple description coding. The adaptation leverages on the fact that multiple descriptions are correlated. Thus if an intermediate node gets feedback telling that another path is likely to deliver a description, this node can compress its description and forward it. Such a compression can also be done already at the source node; however, the feedback arrives more timely and reliably to intermediate nodes that are closer to the final receiver. In this paper we investigate the performance of such adaptation at the source node and an intermediate node, respectively. A trade-off exists between reducing the delay of the feedback by adapting in the vicinity of the receiver and increasing the gain from compression by adapting close to the source. The analysis shows that adaptation in the network provides a better trade-off than adaptation at the source. Schemes which provide simple solutions to adaptation both at the source and in the network are proposed, analyzed, simulated and compared to non-adaptive reference schemes in scenarios that involve last hop that is wireless. The results reveal that the proposed compression schemes offer significant benefits in streaming scenarios.

In this paper, we consider the problem of minimizing a non-smooth convex problem using first-order methods. The number of iterations required to guarantee a certain accuracy for such problems is often excessive and several methods, e.g., restart methods, have been proposed to speed-up the convergence. In the restart method a smoothness parameter is adjusted such that smoother approximations of the original non-smooth problem are solved in a sequence before the original, and the previous estimate is used as the starting point each time. Instead of adjusting the smoothness parameter after each restart, we propose a method where we modify the smoothness parameter in each iteration. We prove convergence and provide simulation examples for two typical signal processing applications, namely total variation denoising and l1-norm minimization. The simulations demonstrate that the proposed method require fewer iterations and show lower complexity compared to the restart method.

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources for mean squared error (MSE) distortion. First, we define the information-theoretic causal rate-distortion function (RDF), Rcit(D). In order to analyze Rcit(D), we introduce Rcit̅(D), the information theoretic causal RDF when reconstruction error is jointly stationary with the source. Based upon Rcit̅(D), we derive four closed form upper bounds to the gap between Rcit̅(D) and Shannon's RDF, two of them strictly smaller than 0.5 bits/sample at all rates. We then show that Rcit̅(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem and propose an iterative procedure to solve it. Finally, we build upon Rcit̅(D) to improve existing bounds on the optimal performance attainable by causal and zero-delay codes.

This paper is about the design and analysis of an index-assignment (IA)-based multiple-description coding scheme for the n-channel asymmetric case. We use entropy constrained lattice vector quantization and restrict attention to simple reconstruction functions, which are given by the inverse IA function when all descriptions are received or otherwise by a weighted average of the received descriptions. We consider smooth sources with finite differential entropy rate and MSE fidelity criterion. As in previous designs, our construction is based on nested lattices which are combined through a single IA function. The results are exact under high-resolution conditions and asymptotically as the nesting ratios of the lattices approach infinity. For any n, the design is asymptotically optimal within the class of IA-based schemes. Moreover, in the case of two descriptions and finite lattice vector dimensions greater than one, the performance is strictly better than that of existing designs. In the case of three descriptions, we show that in the limit of large lattice vector dimensions, points on the inner bound of Pradhan can be achieved. Furthermore, for three descriptions and finite lattice vector dimensions, we show that the IA-based approach yields, in the symmetric case, a smaller rate loss than the recently proposed source-splitting approach.

We consider lossy compression of image sequences using l1-compression with overcomplete dictionaries. As a fidelity measure for the reconstruction quality, we incorporate the recently proposed structural similarity index measure, and we show that this leads to problem formulations that are very similar to conventional l1 compression algorithms. In addition, we develop efficient large-scale algorithms used for joint encoding of multiple image frames.

We consider the problem of lossy compression of images using sparse representations from overcomplete dictionaries. This problem is in principle easy to solve using standard algorithms for convex programming, but often the large dimensions render such an approach intractable. We present a highly efficient method based on recently developed first-order methods, which enables us to compute sparse approximations of entire images with modest time and memory consumption.

We study state estimation via wireless sensor networks over fading channels affected by random packet loss. In the configuration examined, the sensors send their measurements to a single gateway, which decides upon the source coding scheme and the sensor transmitter power levels. The decision process is carried out on-line and adapts to changing channel conditions to achieve an optimal trade-off between estimation quality and sensor energy expenditure. In particular, if some channel conditions are poor, then the gateway commands the corresponding sensors to increase power levels and use multiple-description coding. Simulations based on measured channel data illustrate that the proposed scheme gives excellent results.

In this work, we construct a novel scheme for efficient perceptual coding of audio for robust communication between encoders and wireless hearing aids. To limit the physical size of the hearing aids and to reduce power consumption and thereby increase the lifetime expectancy of the batteries, the hearing aids are constrained to be of low complexity. We therefore provide an asymmetric strategy where most of the computational load is placed at the encoding side. We make use of multiple-description coding. This combats possible erasures on the wireless link between the encoder and the hearing aids without introducing significant delay. Furthermore, we employ psychoacoustically optimized noise-shaping quantizers based on the moving-horizon principle, which exploits a finite prediction horizon.

We address the connection between the multiple-description (MD) problem and Delta–Sigma quantization. The inherent redundancy due to oversampling in Delta–Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise-shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically, as the dimension of the lattice vector quantizer and order of the noise-shaping filter approach infinity, the entropy rate of the dithered Delta–Sigma quantization scheme approaches the symmetric two-channel MD rate–distortion function for a memoryless Gaussian source and mean square error (MSE) fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise-shaping filter must be minimum phase and have a piecewise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.

We characterize the rate-distortion function for zero-mean stationary Gaussian sources under the MSE fidelity criterion and subject to the additional constraint that the distortion is uncorrelated to the input. The solution is given by two equations coupled through a single scalar parameter. This has a structure similar to the well known water-filling solution obtained without the uncorrelated distortion restriction. Our results fully characterize the unique statistics of the optimal distortion. We also show that, for all positive distortions, the minimum achievable rate subject to the uncorrelation constraint is strictly larger than that given by the un-constrained rate-distortion function. This gap increases with the distortion and tends to infinity and zero, respectively, as the distortion tends to zero and infinity.

It was recently shown that the symmetric multiple-description (MD) quadratic rate-distortion function for memoryless Gaussian sources and two descriptions can be achieved by dithered Delta-Sigma quantization combined with memoryless entropy coding. In this paper,we generalize this result to stationary (colored) Gaussian sources by combining noise shaping and source prediction. We first propose a new representation for the test channel that realizes the MD rate-distortion function of a Gaussian source, both in the white and in the colored source case. We then show that this test channel canbe materialized by embedding two source prediction loops, one for each description, within a common noise shaping loop. While the noise shaping loop controls the tradeoff between the side and the central distortions, the role of prediction (like in differential pulse code modulation) is to extract the source innovations from the reconstruction at each of the side decoders, and thus reduce the coding rate. Finally, we show that this scheme achieves the MD rate-distortion function at all resolutions and all side-to-central distortion ratios, in the limit of high dimensional quantization.

In this paper we address the connection between the multiple-description (MD) problem and delta-sigma quantization. Specifically, we exploit the inherent redundancy due to oversampling in delta-sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, in order to construct a symmetric MD coding scheme. We show that the use of feedback by means of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, we show that the symmetric two-channel MD rate-distortion function for the memoryless Gaussian source and MSE fidelity criterion can be achieved at any resolution. This realization provides a new interesting interpretation for the information theoretic solution. The proposed design is symmetric in rate by construction and there is therefore no need for source splitting

We consider the problem of reliable distribution of audio over packet-switched networks. We make use of multiple-description coding combined with transform coding in order to obtain robustness towards packet losses. Previous approaches to this problem were restricted to the case of only two descriptions. In this work we use n-channel multiple-description lattice vector quantizers (MD-LVQs), which allow for the possibility of using more than two descriptions. For a given packet-loss probability we find the number of descriptions and the bit allocation between transform coefficients which minimizes a perceptual distortion measure subject to an entropy constraint. The optimal quantizers are presented in closed form, thus avoiding any iterative quantizer design procedures. The theoretical results are verified with numerical computer simulations using audio signals and it is shown that in environments with excessive packet losses it is advantageous to use more than two descriptions. We verify in subjective listening tests that using more than two descriptions lead to signals of perceptually higher quality

It was recently shown that a subset of the rate distortion region of the symmetric K-channel multiple description coding problem can be achieved by use of (K, k) source-channel erasure codes (SCEC). The construction of the previously proposed SCEC made use of source coding with side information and relied upon random codebooks. In this paper we propose to replace the random codebooks of (K, k) SCEC by structured (lattice) codebooks. We then show that, in certain cases and under high-resolution assumptions, this improves the achievable rate distortion region over the traditional (K, k) SCEC

In this paper, we derive analytical expressions for the central and side quantizers which, under high-resolution assumptions, minimize the expected distortion of a symmetric multiple-description lattice vector quantization (MD-LVQ) system subject to entropy constraints on the side descriptions for given packet-loss probabilities. We consider a special case of the general n-channel symmetric multiple-description problem where only a single parameter controls the redundancy tradeoffs between the central and the side distortions. Previous work on two-channel MD-LVQ showed that the distortions of the side quantizers can be expressed through the normalized second moment of a sphere. We show here that this is also the case for three-channel MD-LVQ. Furthermore, we conjecture that this is true for the general n-channel MD-LVQ. For given source, target rate, and packet-loss probabilities we find the optimal number of descriptions and construct the MD-LVQ system that minimizes the expected distortion. We verify theoretical expressions by numerical simulations and show in a practical setup that significant performance improvements can be achieved over state-of-the-art two-channel MD-LVQ by using three-channel MD-LVQ.

We derive analytical expressions for the central and side quantizers in an n-channel symmetric multiple-description lattice vector quantizer which, under high-resolution assumptions, minimize the expected distortion subject to entropy constraints on the side descriptions for given packet-loss probabilities. The performance of the central quantizer is lattice dependent whereas the performance of the side quantizers is lattice independent. In fact the normalized second moments of the side quantizers are given by that of an L-dimensional sphere. Furthermore, our analytical results reveal a simple way to determine the optimum number of descriptions. We verify theoretical results with numerical experiments and show that with a packet-loss probability of 5%, a gain of 9.1 dB in MSE over state-of-the-art two-description systems can be achieved when quantizing a two-dimensional unit-variance Gaussian source using a total bit budget of 15 bits/dimension and using three descriptions. With 20% packet loss, a similar experiment reveals an MSE reduction of 10.6 dB when using four descriptions.

We present analytical expressions for optimal entropy-constrained multiple-description lattice vector quantizers which, under high-resolutions assumptions, minimize the expected distortion for given packet-loss probabilities. We consider the asymmetric case where packet-loss probabilities and side entropies are allowed to be unequal and find optimal quantizers for any number of descriptions in any dimension. We show that the normalized second moments of the side-quantizers are given by that of an L-dimensional sphere independent of the choice of lattices. Furthermore, we show that the optimal bit-distribution among the descriptions is not unique. In fact, within certain limits, bits can be arbitrarily distributed

Recently, lattice vector quantizers (LVQ) capable of performing close to known information theoretic bounds were introduced in the area of multiple description coding (MDC). We derive analytical expressions for the central and side quantizers which minimize the expected distortion of an LVQ subject to entropy constraints on the side descriptions for given packet loss probabilities. We show that for certain packet loss probabilities, an optimal LVQ for single descriptions might not be optimal for multiple descriptions. Specifically, we show that the Z/sup 2/ lattice performs better than the A/sub 2/ lattice in some cases. Moreover, our results suggest a practical way of determining which lattice quantizers are optimal for given packet loss probabilities.