arXiv subjects

Jan Østergaard

Publications and source records attributed to Jan Østergaard.

53 records · Page 3Linked to original sources

arXiv2021

Deep Sound Field Reconstruction in Real Rooms: Introducing the ISOBEL Sound Field Dataset

Knowledge of loudspeaker responses are useful in a number of applications, where a sound system is located inside a room that alters the listening experience depending on position within the room. Acquisition of sound fields for sound sources located in reverberant rooms can be achieved through labor intensive measurements of impulse response functions covering the room, or alternatively by means of reconstruction methods which can potentially require significantly fewer measurements. This paper extends evaluations of sound field reconstruction at low frequencies by introducing a dataset with measurements from four real rooms. The ISOBEL Sound Field dataset is publicly available, and aims to bridge the gap between synthetic and real-world sound fields in rectangular rooms. Moreover, the paper advances on a recent deep learning-based method for sound field reconstruction using a very low number of microphones, and proposes an approach for modeling both magnitude and phase response in a U-Net-like neural network architecture. The complex-valued sound field reconstruction demonstrates that the estimated room transfer functions are of high enough accuracy to allow for personalized sound zones with contrast ratios comparable to ideal room transfer functions using 15 microphones below 150 Hz.

cs.SD↗

arXiv2021

An Orthogonality Principle for Select-Maximum Estimation of Exponential Variables

It was recently proposed to encode the one-sided exponential source X via K parallel channels, Y1, ..., YK , such that the error signals X - Yi, i = 1,...,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{Y1,..., YK}. 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 Y1,...,YK.

cs.IT↗

arXiv2020

Estimating Conditional Transfer Entropy in Time Series using Mutual Information and Non-linear Prediction

We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of new information and improvement of the prediction accuracy provided by the variables. Then, using a greedy approach, the most informative subsets are selected in an iterative way. The algorithm terminates, when the highest ranked variable is not able to significantly improve the accuracy of the prediction as compared to that obtained using the existing selected subsets. In a simulation study, we compare our estimator to existing state-of-the-art methods at different data lengths and directed dependencies strengths. It is demonstrated that the proposed estimator has a significantly higher accuracy than that of existing methods, especially for the difficult case, where the data is highly correlated and coupled. Moreover, we show its false detection of directed dependencies due to instantaneous couplings effect is lower than that of existing measures. We also show applicability of the proposed estimator on real intracranial electroencephalography data.

stat.ME↗

arXiv2018

Information Loss in the Human Auditory System

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 get lost. In this paper, we aim at quantifying the 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. Towards 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 sub-optimal for recognizing noisy words.

cs.IT↗

arXiv2018

Stationarity in the Realizations of the Causal Rate-Distortion Function for One-Sided Stationary Sources

This paper derives novel results on the characterization of the the causal information rate-distortion function (IRDF) $R_{c}^{it}(D)$ for arbitrarily-distributed one-sided stationary $κ$-th order Markov source x(1),x(2),.... It is first shown that Gorbunov and Pinsker's results on the stationarity of the realizations to the causal IRDF (stated for two-sided stationary sources) do not apply to the commonly used family of asymptotic average single-letter (AASL) distortion criteria. Moreover, we show that, in general, a reconstruction sequence cannot be both jointly stationary with a one-sided stationary source sequence and causally related to it. This implies that, in general, the causal IRDF for one-sided stationary sources cannot be realized by a stationary distribution. However, we prove that for an arbitrarily distributed one-sided stationary source and a large class of distortion criteria (including AASL), the search for $R_{c}^{it}(D)$ can be restricted to distributions which yield the output sequence y(1), y(2),... jointly stationary with the source after $κ$ samples. Finally, we improve the definition of the stationary causal IRDF $\overline{R}_{c}^{it}(D)$ previously introduced by Derpich and Østergaard for two-sided Markovian stationary sources and show that $\overline{R}_{c}^{it}(D)$ for a two-sided source ...,x(-1),x(0),x(1),... equals $R_{c}^{it}(D)$ for the associated one-sided source x(1), x(2),.... This implies that, for the Gaussian quadratic case, the practical zero-delay encoder-decoder pairs proposed by Derpich and Østergaard for approaching $R_{c}^{it}(D)$ achieve an operational data rate which exceeds $R_{c}^{it}(D)$ by less than $1+0.5 \log_2(2 πe /12) \simeq 1.254$ bits per sample.

cs.IT↗

arXiv2017

Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels

The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.

eess.SY↗

arXiv2016

Delay Minimization in Real-time Communications with Joint Buffering and Coding

We present a closed-form expression for the minimal delay that is achievable in a setting that combines a buffer and an erasure code, used to mitigate the packet delay variance. The erasure code is modeled according to the recent information-theoretic results on finite block length codes. Evaluations reveal that accurate knowledge of the network parameters is essential for optimal operation. Moreover, it is shown that, when the network packet delay variance is large, the buffer delay becomes negligible. Therefore, in this case the delay budget should be spent mainly on the erasure code.

cs.IT↗

arXiv2016

Source Coding in Networks with Covariance Distortion Constraints

We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.

cs.IT↗

arXiv2016

On the Construction of Jointly Superregular Lower Triangular Toeplitz Matrices

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(2^p) for the case of matrices with dimensions less than or equal to 5 x 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.

cs.IT↗

arXiv2015

The Entropy Gain of Linear Time-Invariant Filters and Some of its Implications

We study the increase in per-sample differential entropy rate of random sequences and processes after being passed through a non minimum-phase (NMP) discrete-time, linear time-invariant (LTI) filter G. For such filters and random processes, it has long been established that this entropy gain, Gain(G), equals the integral of log|G(exp(jw))|. It is also known that, if the first sample of the impulse response of G has unit-magnitude, then this integral equals the sum of the logarithm of the magnitudes of the non-minimum phase zeros of G, say B(G). In this note, we begin by showing that existing time-domain proofs of these results, which consider finite length-n sequences and then let n tend to infinity, have neglected significant mathematical terms and, therefore, are inaccurate. We discuss some of the implications of this oversight when considering random processes. We then present a rigorous time-domain analysis of the entropy gain of LTI filters for random processes. In particular, we show that the entropy gain between equal-length input and output sequences is upper bounded by B(G) and arises if and only if there exists an output additive disturbance with finite differential entropy (no matter how small) or a random initial state. Instead, when comparing the input differential entropy to that of the entire (longer) output of G, the entropy gain equals B(G) without the need for additional exogenous random signals. We illustrate some of the consequences of these results by presenting their implications in three different problems. Specifically: a simple derivation of the rate-distortion function for Gaussian non-stationary sources, conditions for equality in an information inequality of importance in networked control problems, and an observation on the capacity of auto-regressive Gaussian channels with feedback.

cs.IT↗

arXiv2015

Shaped Gaussian Dictionaries for Quantized Networked Control Systems with Correlated Dropouts

This paper studies fixed rate vector quantisation for noisy networked control systems (NCSs) with correlated packet dropouts. In particular, a discrete-time linear time invariant system is to be controlled over an error-prone digital channel. The controller uses (quantized) packetized predictive control to reduce the impact of packet losses. The proposed vector quantizer is based on sparse regression codes (SPARC), which have recently been shown to be efficient in open-loop systems when coding white Gaussian sources. The dictionaries in existing design of SPARCs consist of independent and identically distributed (i.i.d.) Gaussian entries. However, we show that a significant gain can be achieved by using Gaussian dictionaries that are shaped according to the second-order statistics of the NCS in question. Furthermore, to avoid training of the dictionaries, we provide closed-form expressions for the required second-order statistics in the absence of quantization.

math.OC↗

arXiv2013

Fundamental Inequalities and Identities Involving Mutual and Directed Informations in Closed-Loop Systems

We present several novel identities and inequalities relating the mutual information and the directed information in systems with feedback. The internal blocks within such systems are restricted only to be causal mappings, but are allowed to be non-linear, stochastic and time varying. Moreover, the involved signals can be arbitrarily distributed. We bound the directed information between signals inside the feedback loop by the mutual information between signals inside and outside the feedback loop. This fundamental result has an interesting interpretation as a law of conservation of information flow. Building upon it, we derive several novel identities and inequalities, which allow us to prove some existing information inequalities under less restrictive assumptions. Finally, we establish new relationships between nested directed informations inside a feedback loop. This yields a new and general data-processing inequality for systems with feedback.

cs.IT↗

arXiv2012

Design and Analysis of LT Codes with Decreasing Ripple Size

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.

cs.IT↗

arXiv2012

Analysis of LT Codes with Unequal Recovery Time

In this paper we analyze a specific class of rateless codes, called LT codes with unequal recovery time. These codes provide the option of prioritizing different segments of the transmitted data over other. The result is that segments are decoded in stages during the rateless transmission, where higher prioritized segments are decoded at lower overhead. Our analysis focuses on quantifying the expected amount of received symbols, which are redundant already upon arrival, i.e. all input symbols contained in the received symbols have already been decoded. This analysis gives novel insights into the probabilistic mechanisms of LT codes with unequal recovery time, which has not yet been available in the literature. We show that while these rateless codes successfully provide the unequal recovery time, they do so at a significant price in terms of redundancy in the lower prioritized segments. We propose and analyze a modification where a single intermediate feedback is transmitted, when the first segment is decoded in a code with two segments. Our analysis shows that this modification provides a dramatic improvement on the decoding performance of the lower prioritized segment.

cs.IT↗

arXiv2011

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

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 (MSE) 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 $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2πe) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(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\leq σ_{x}^{2}, \bar{Rc^{it}}(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. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...

cs.IT↗

arXiv2010

On the Role of Feedback in LT Codes

This paper concerns application of feedback in LT codes. The considered type of feedback is acknowledgments, where information on which symbols have been decoded is given to the transmitter. We identify an important adaptive mechanism in standard LT codes, which is crucial to their ability to perform well under any channel conditions. We show how precipitate application of acknowledgments can interfere with this adaptive mechanism and lead to significant performance degradation. Moreover, our analysis reveals that even sensible use of acknowledgments has very low potential in standard LT codes. Motivated by this, we analyze the impact of acknowledgments on multi layer LT codes, i.e. LT codes with unequal error protection. In this case, feedback proves advantageous. We show that by using only a single feedback message, it is possible to achieve a noticeable performance improvement compared to standard LT codes.

cs.IT↗

arXiv2010

Bounding the Rate Region of Vector Gaussian Multiple Descriptions with Individual and Central Receivers

In this work, the rate region of the vector Gaussian multiple description problem with individual and central quadratic distortion constraints is studied. In particular, an outer bound to the rate region of the L-description problem is derived. The bound is obtained by lower bounding a weighted sum rate for each supporting hyperplane of the rate region. The key idea is to introduce at most L-1 auxiliary random variables and further impose upon the variables a Markov structure according to the ordering of the description weights. This makes it possible to greatly simplify the derivation of the outer bound. In the scalar Gaussian case, the complete rate region is fully characterized by showing that the outer bound is tight. In this case, the optimal weighted sum rate for each supporting hyperplane is obtained by solving a single maximization problem. This contrasts with existing results, which require solving a min-max optimization problem.

cs.IT↗