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Norbert Goertz

dblp:g/NorbertGoertz · also Norbert Görtz · DBLP profile ↗
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48ranked-venue papers
10as first author
0since 2021 · last 2020
—ORCID · none

Domains — the database's venue-derived domains; a paper can count in several

Computer networks · 17 · 2 first-authorGraphics, computer vision, multimedia, augmented reality and games · 17 · 5 first-authorApplied, interdisciplinary, general and emerging computing · 6 · 2 first-authorTheory of computation · 4Artificial intelligence and machine learning · 3 · 2 first-authorDatabases, data management, data science and information retrieval · 2

Expertise — from the expertise taxonomy: the topics of the expert's papers under the CCF categories. A weight counts papers with recency: 1 for a paper about the topic, 0.3 when the topic is its context, halved every five years.

Theoretical computer science
7 papers
Coding theory · 61% Mathematical optimization · 23% Information theory · 16%
Computer graphics and multimedia
1 paper
Audio and music processing · 100%
Databases, data mining, and information retrieval
1 paper
Data mining · 100%

Topics — the 24 heaviest of 26, each with the papers that count most for it

TopicWeightPapersLastEvidence papers
Mathematical optimization › sparse learning
dictionary learning
0.212016
On the Minimax Risk of Dictionary Learning · IEEE Trans. Inf. Theory 2016
Information theory › estimation theory
minimax risk
0.212016
On the Minimax Risk of Dictionary Learning · IEEE Trans. Inf. Theory 2016
Mathematical optimization › sparse optimization
sparse coding
0.212016
On the Minimax Risk of Dictionary Learning · IEEE Trans. Inf. Theory 2016
Coding theory
source coding
0.232007
On the BCJR Algorithm for Rate-Distortion Source Coding · IEEE Trans. Inf. Theory 2007
Linear Congruential Trellis Source Codes: Design and Analysis · IEEE Trans. Commun. 2007
Optimization of the index assignments for multiple description vector quantizers · IEEE Trans. Commun. 2003
Coding theory › error-correcting codes
LDPC codes
0.212013
Robust Rate-Compatible Punctured LDPC Convolutional Codes · IEEE Trans. Commun. 2013
Coding theory › error-correcting codes › LDPC codes
LDPC convolutional codes
0.212013
Robust Rate-Compatible Punctured LDPC Convolutional Codes · IEEE Trans. Commun. 2013
Coding theory › error-correcting codes › LDPC codes
rate-compatible puncturing
0.212013
Robust Rate-Compatible Punctured LDPC Convolutional Codes · IEEE Trans. Commun. 2013
Audio and music processing
speech analysis
0.112012
Nonlinear Long-Term Prediction of Speech Based on Truncated Volterra Series · IEEE Trans. Speech Audio Process. 2012
Coding theory › source coding › quantization
trellis source coding
0.122007
On the BCJR Algorithm for Rate-Distortion Source Coding · IEEE Trans. Inf. Theory 2007
Linear Congruential Trellis Source Codes: Design and Analysis · IEEE Trans. Commun. 2007
Coding theory › error-correcting codes › decoding
iterative decoding
0.122013
Robust Rate-Compatible Punctured LDPC Convolutional Codes · IEEE Trans. Commun. 2013
On the iterative approximation of optimal joint source-channel decoding · IEEE J. Sel. Areas Commun. 2001
Data mining
representation learning
0.112016
On the Minimax Risk of Dictionary Learning · IEEE Trans. Inf. Theory 2016
Coding theory › error-correcting codes › decoding › iterative decoding › soft-input soft-output decoding
BCJR algorithm
0.112007
On the BCJR Algorithm for Rate-Distortion Source Coding · IEEE Trans. Inf. Theory 2007
Coding theory › source coding
lossy source coding
0.112007
On the BCJR Algorithm for Rate-Distortion Source Coding · IEEE Trans. Inf. Theory 2007
Coding theory › source coding
rate-distortion theory
0.112007
Linear Congruential Trellis Source Codes: Design and Analysis · IEEE Trans. Commun. 2007
Coding theory › source coding › quantization › structured vector quantization
trellis-coded quantization
0.112007
Linear Congruential Trellis Source Codes: Design and Analysis · IEEE Trans. Commun. 2007
Coding theory › source coding › multiterminal source coding
multiple description coding
0.012003
Optimization of the index assignments for multiple description vector quantizers · IEEE Trans. Commun. 2003
Coding theory › source coding › quantization
vector quantization
0.012003
Optimization of the index assignments for multiple description vector quantizers · IEEE Trans. Commun. 2003
Coding theory
joint source-channel coding
0.012001
On the iterative approximation of optimal joint source-channel decoding · IEEE J. Sel. Areas Commun. 2001
Coding theory › error-correcting codes › decoding › decoding algorithms
joint source-channel decoding
0.012001
On the iterative approximation of optimal joint source-channel decoding · IEEE J. Sel. Areas Commun. 2001
Coding theory › error-correcting codes › decoding
channel decoding
0.012007
On the BCJR Algorithm for Rate-Distortion Source Coding · IEEE Trans. Inf. Theory 2007
Mathematical optimization
discrete optimization
0.012003
Optimization of the index assignments for multiple description vector quantizers · IEEE Trans. Commun. 2003
Coding theory › source coding › quantization › vector quantization
index assignment
0.012003
Optimization of the index assignments for multiple description vector quantizers · IEEE Trans. Commun. 2003
Information theory
channel capacity
0.012001
On the iterative approximation of optimal joint source-channel decoding · IEEE J. Sel. Areas Commun. 2001
Coding theory › joint source-channel coding
source-channel separation
0.012001
On the iterative approximation of optimal joint source-channel decoding · IEEE J. Sel. Areas Commun. 2001

Methods — techniques the papers use, named apart from their topics

restricted isometry property · 0.5minimax estimation · 0.5information-theoretic bounds · 0.5puncturing design · 0.2cycle analysis · 0.2volterra series · 0.1second-order volterra filter · 0.1cumulative distribution function correction · 0.1trellis symmetry analysis · 0.1recursion properties · 0.1random search · 0.1BCJR algorithm · 0.1
YearPublicationVenuePosition
2020 VAMP with Vector-Valued Diagonalization
abstract
Vector approximate message passing is studied where vectorvalued diagonalization instead of a uniform one is employed. Thereby,individualvariancesare tracked within the algorithm instead of an average one. Straightforward application based on the expectation-consistent approximate inference framework does not give satisfactory results. The main reason for this is that the precision parameters may become negativeduring the iterations. In this contribution, improved versions for the update equation ("Onsager correction") are derived from basic estimation principles. Numerical simulations cover the superiority of the new variants.
Robert F. H. Fischer, Carmen Sippel, Norbert Goertz
ICASSP3
2019 Robust Approximate Message Passing for Nonzero-mean Sensing Matrices
abstract
The standard Approximate Message Passing (AMP) algorithm efficiently recovers a sparse signal from a small number of noisy linear measurements. It requires the measurement matrix to be zero-mean, however. Even small deviations from this requirement cause it to diverge. In this paper, we show how mean-removal can be combined with standard Bayesian AMP to achieve signal recovery. Furthermore, a modified Bayesian AMP algorithm is presented, which achieves performance comparable to AMP in the zero-mean measurement matrix regime even for large mean. Simulation results and state evolution for both techniques are provided.
Stefan C. Birgmeier, Norbert Goertz
ICASSP2
2017 Smooth graph signal recovery via efficient Laplacian solvers
abstract
We consider the problem of recovering a smooth graph signal from noisy samples observed at a small number of nodes. The signal recovery is formulated as a convex optimization problem using Tikhonov regularization based on the graph Laplacian quadratic form. The optimality conditions for this optimization problem form a system of linear equations involving the graph Laplacian. We solve this linear system via the iterative Gauss-Seidel method, which is shown to be particularly well-suited for smooth graph signal recovery. The effectiveness of the proposed recovery method is verified by numerical experiments using a real-world data-set.
Gita Babazadeh Eslamlu, Alexander Jung 0001, Norbert Goertz
ICASSP3
2017 Sampled graph-signals: Iterative recovery with an analytic error bound
abstract
Recovery of graph signals from a limited number of sampled components is investigated. An iterative recovery algorithm is motivated and derived, including an analytic upper bound for the error. Simulation results are also presented.
Norbert Goertz
ISIT1
2016 Graph signal recovery from incomplete and noisy information using approximate message passing
abstract
We consider the problem of recovering a graph signal from noisy and incomplete information. In particular, we propose an approximate message passing based iterative method for graph signal recovery. The recovery of the graph signal is based on noisy signal values at a small number of randomly selected nodes. Our approach exploits the smoothness of typical graph signals occurring in many applications, such as wireless sensor networks or social network analysis. The graph signals are smooth in the sense that neighboring nodes have similar signal values. Methodologically, our algorithm is a new instance of the denoising based approximate message passing framework introduced recently by Metzler et. al. We validate the performance of the proposed recovery method via numerical experiments. In certain scenarios our algorithm outperforms existing methods.
Gita Babazadeh Eslamlu, Alexander Jung 0001, Norbert Goertz, Mehdi Fereydooni
ICASSP3
2016 On the Minimax Risk of Dictionary Learning
abstract
We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity of the dictionary learning (DL) schemes. By casting DL as a classical (or frequentist) estimation problem, the lower bounds on the worst case MSE are derived following an established information-theoretic approach to minimax estimation. The main contribution of this paper is the adaption of these information-theoretic tools to the DL problem in order to derive lower bounds on the worst case MSE of any DL algorithm. We derive three different lower bounds applying to different generative models for the observed signals. The first bound only requires the existence of a covariance matrix of the (unknown) underlying coefficient vector. By specializing this bound to the case of sparse coefficient distributions and assuming the true dictionary satisfies the restricted isometry property, we obtain a lower bound on the worst case MSE of DL methods in terms of the signal-to-noise ratio (SNR). The third bound applies to a more restrictive subclass of coefficient distributions by requiring the non-zero coefficients to be Gaussian. Although the applicability of this bound is the most limited, it is the tightest of the three bounds in the low SNR regime. A particular use of our lower bounds is the derivation of necessary conditions on the required number of observations (sample size), such that DL is feasible, i.e., accurate DL schemes might exist. By comparing these necessary conditions with sufficient conditions on the sample size such that a particular DL technique is successful, we are able to characterize the regimes, where those algorithms are optimal in terms of required sample size.
Alexander Jung 0001, Yonina C. Eldar, Norbert Goertz
IEEE Trans. Inf. Theory3
2016 RFID Tag Acquisition Via Compressed Sensing: Fixed vs. Random Signature Assignment
abstract
We introduce a novel scheme to perform radio frequency identification (RFID) with compressed sensing techniques. The proposed scheme allows quick and reliable identification of several RFID tags, even at low signal-to-noise ratio. Contrary to the widely used frame slotted ALOHA (FSA) protocol, the tags activated by a reader deliberately respond simultaneously with their assigned signature during the acquisition phase; collisions are regarded as beneficial rather than destructive. The signatures are drawn from a huge signature pool, and the set of signatures that is assigned to the activated tags is very small compared to the total signature count. This introduces sparsity to the acquisition phase which, in turn, allows formulation of the acquisition as a compressed sensing measurement. Furthermore, our formulation permits the usage of a low-complexity approximate message passing algorithm for compressed sensing recovery. We compare two realizations of the compressed sensing-based approach to the FSA protocol. The first performs fixed signature assignment - this enables very quick identification but sacrifices flexibility. The second performs random signature assignment - this reduces the identification speed but provides flexibility. A comparison via simulation shows that both compressed sensing-based approaches significantly outperform FSA in terms of identification speed and robustness to noise.
Martin Mayer, Norbert Goertz
IEEE Trans. Wirel. Commun.2
2015 Graphical LASSO based Model Selection for Time Series
Alexander Jung 0001, Gabor Hannak, Norbert Goertz
IEEE Signal Process. Lett.3
2015 Statistical Analysis of Multiantenna Relay Systems and Power Allocation Algorithms in a Relay With Partial Channel State Information
abstract
The performance of a dual-hop MIMO relay network is studied in this paper. The relay is assumed to have access to the statistical channel state information of its preceding and following channels, and it is assumed that fading at the antennas of the relay is correlated. The cumulative density function (cdf) of the received SNR at the destination is first studied, and closed-form expressions are derived for the asymptotic cases of the fully correlated and noncorrelated scenarios; moreover, the statistical characteristics of the SNR are further studied, and an approximate cdf of the SNR is derived for arbitrary correlation. The cdf is a multipartite function, which does not easily lend itself to further mathematical calculations, e.g., rate optimization. However, we use it to propose a simple power allocation algorithm, which we call “proportional power allocation.” The algorithm is explained in detail for the case of two antennas and three antennas at the relay, and the extension of the algorithm to a relay with an arbitrary number of the antennas is discussed. Although the proposed method is not claimed to be optimal, the result is indistinguishable from the benchmark obtained using exhaustive search. The simplicity of the algorithm combined with its precision is indeed attractive from the practical point of view.
Mehdi M. Molu, Alister Burr, Norbert Goertz
IEEE Trans. Wirel. Commun.3
2014 Iterative Recovery of Dense Signals from Incomplete Measurements
abstract
Within the framework of compressed sensing, we consider dense signals, which contain both discrete as well as continuous-amplitude components. We demonstrate by a comprehensive numerical study–to the best of our knowledge the first of its kind in the literature–that dense signals can be recovered from noisy, incomplete linear measurements by simple iterative algorithms that are inspired by or are implementations of approximate message passing. Those iterative algorithms are shown to significantly outperform all other algorithms presented so far, when they use a novel noise-adaptive thresholding function that is proposed in this contribution.
Norbert Goertz, Chunli Guo, Alexander Jung 0001, Mike E. Davies 0001, Gerhard Doblinger
IEEE Signal Process. Lett.1
2014 Optimal Precoding in the Relay and the Optimality of Largest Eigenmode Relaying with Statistical Channel State Information
abstract
An optimal precoding method for a multiple antenna relay node is investigated in order to maximize the achievable rate of the cooperative communication system. It is assumed that only the channel covariance matrices of the relay's receive and transmit channels are available to the relay and that the antennas of the relay are correlated. It is shown that the optimal transmission from the relay should be conducted in the direction of the eigenvectors of the channel covariance matrix. Moreover, necessary and sufficient conditions are derived under which the relay transmission achieves capacity by transmitting from the strongest eigenvector only; this method is called Largest Eigenmode Relaying (LER). The exact result contains an expectation operation that needs to be solved numerically; to reduce the computational complexity, novel methods are proposed that lead to closed-form solutions. A lower bound for the optimal region of LER is derived. Moreover, the effect of the number of source antennas on the optimality of LER is investigated asymptotically. The simulation results show very little difference between the regions in which LER is optimal when the source is equipped with a finite or an infinite number of antennas.
Mehdi M. Molu, Norbert Goertz
IEEE Trans. Wirel. Commun.2
2013 Power-controlled cross-layer scheduling
abstract
Power-Controlled Cross-Layer Scheduling is proposed for real-time multimedia-applications in cellular wireless networks. The new scheme borrows elements from Proportional Fair Scheduling, from which it differs in that it can satisfy hard delay constraints, and improves on exploiting multiuser diversity gains by selectively excluding users from scheduling decisions based on their rate demands. The performance of the new scheduler is compared to performance bounds from multiuser information theory. Then, the basic concept is extended to a real-world scenario, in which the long-term path losses of all users will change over time: this necessitates the introduction of a power control scheme, that, if carefully designed, “inverts” the long-term pathloss of the channel, but not the fast fading. An analysis of the outage probability characteristic shows near-optimum behavior for delay-constrained applications and reveals huge performance gains for demanding users, compared to classical proportional fair scheduling.
Johannes Gonter, Norbert Goertz
ICC2
2013 Optimality range of Largest Eigenmode Relaying with partial channel state information in the relay
abstract
Optimal precoding in the relay with partial channel state information in the relay is studied in this paper. It is assumed that the antennas of the relay are correlated. Transmission only via the eigenvector corresponding to the largest eigenvalue of the correlation matrix is investigated in this paper which is called Largest Eigenmode Relaying (LER). We derive necessary and sufficient condition under which the transmission achieves capacity only by LER. Although the derived condition requires computationally expensive Monte Carlo simulations to be validated, an alternative method is introduced to circumvent the Monte Carlo simulations: we evaluate a system with infinite number of antennas in the source and derive a closed-form necessary and sufficient condition under which LER is optimal. It is observed, by simulations, that the optimality region of LER is almost independent of the number of antennas in the source; hence, the LER optimality condition derived for infinite number of the antennas in the source can, alternatively, be exploited for systems with finite number of antennas in the source with insignificant difference.
Mehdi M. Molu, Norbert Goertz
ISIT2
2013 EWMA-triggered waterfilling for reduced-complexity resource management in ad-hoc connections
abstract
This paper introduces a highly efficient waterfilling-based strategy for optimal use of the channel in vehicular or personal ad-hoc communications. The approach provides near optimum allocation of resources and enables small communications devices to establish connections when the energy efficiency is at its best. Instead of calculating the transmit power through conventional waterfilling, the proposed algorithm calculates the waterlevel, thus providing a decision threshold and a strategy for optimum use of the time-variant channel at the same time. The algorithm adapts to the changing average channel quality by applying an exponentially-weighted moving-average (EWMA) trigger to re-calculate the waterlevel. The new algorithm is compared to an efficient non-iterative algorithm that directly calculates the transmit powers in every time-slot. It is shown that the new strategy reduces computation time by approximately 90% compared to the classic approach without compromising performance measures such as transmitted information or energy. Practical implementation is briefly discussed to demonstrate suitability of the algorithm for integration into tomorrow's communication devices.
Johannes Gonter, Norbert Goertz, Markus Rupp, Wolfgang Gartner
PIMRC2
2013 An Analytical Approach to the Outage Probability of Amplify-and-Forward Relaying with an MRC Receiver
abstract
A novel analytical approach is proposed for the performance analysis of AF relaying systems with MRC receiver in the destination. We first derive PDF and CDF of equivalent SNR of the equivalent S-R-D channel. However, both the PDF and CDF include modified Bessel functions which are not easily tractable. In order to derive an analytical statistical model for the PDF of the total SNR at the output of MRC receiver, a novel approach is introduced to rewrite the modified Bessel function of second kind in the form of infinite series using simple elementary functions. By substituting novel series representation of modified Bessel function in the PDF of equivalent S-R-D channel, the performance of the overall system which includes MRC combining in the destination is analytically studied and closed form expressions are derived for the outage probability of the system. Interestingly, the infinite series approaches its asymptotic result rather accurately with a few terms only. Numerical simulations are provided to verify the accuracy of the novel theoretical approach.
Mehdi M. Molu, Norbert Goertz
VTC Spring2
2013 Robust Rate-Compatible Punctured LDPC Convolutional Codes
abstract
A family of robust rate-compatible (RC) punctured low-density parity-check convolutional codes (LDPC-CCs) is derived from a time-invariant LDPC-CC mother code by periodically puncturing encoded bits (variable nodes) with respect to several criteria: (1) ensuring the recoverability of punctured variable nodes, (2) minimizing the number of completely punctured cycle trapping sets (CPCTSs), and (3) minimizing the number of punctured variable nodes involved in short cycles. The influence of (1) and (3) on iterative decoding performance is felt most strongly in the waterfall region of the bit-error-rate (BER) curve, while (2) has a larger effect in the error floor, or high signal-to-noise ratio (SNR), region. We show that the length of the puncturing period is an important parameter when designing high rate punctured codes and, moreover, that extending the puncturing period can improve the decoding performance and extend the range of compatible rates. As examples, we obtain families of RC LDPC-CCs from several time-invariant LDPC-CC mother codes with monomial and binomial entries in their polynomial syndrome former matrices.
David G. M. Mitchell, Norbert Goertz, Daniel J. Costello Jr.
IEEE Trans. Commun.3
2012 Distance spectrum estimation of LDPC convolutional codes
abstract
Time-invariant low-density parity-check convolutional codes (LDPC-CCs) derived from corresponding quasi-cyclic (QC) LDPC block codes (LDPC-BCs) can be described by a polynomial syndrome former matrix (polynomial-domain transposed parity-check matrix). In this paper, an estimation of the distance spectrum of time-invariant LDPC-CCs is obtained by splitting the polynomial syndrome former matrix into submatrices representing “super codes” and then evaluating the linear dependence between codewords of the corresponding super codes. This estimation results in an upper bound on the minimum free distance of the original code and, additionally, a lower bound on the number of codewords Awwith Hamming weight w.
David G. M. Mitchell, Norbert Goertz, Daniel J. Costello Jr.
ISIT3
2012 Nonlinear Long-Term Prediction of Speech Based on Truncated Volterra Series
abstract
Previous studies of nonlinear prediction of speech have been mostly focused on short-term prediction. This paper presents long-term nonlinear prediction based on second-order Volterra filters. It will be shown that the presented predictor can outperform conventional linear prediction techniques in terms of prediction gain and “whiter” residuals.
Vladimir Despotovic, Norbert Goertz, Zoran H. Peric
IEEE Trans. Speech Audio Process.2
2011 Limits on Information Transmission in Vehicle-to-Vehicle Communication
abstract
We investigate limits on information transmission in vehicle-to-vehicle or vehicle-to-mesh communication. We quantify and maximise by appropriate transmit power allocation an upper bound for the amount of information that can be transmitted during the "lifetime" of the channel, whose classical Shannon capacity would be zero. We also introduce more practical causal power allocation schemes and evaluate their performance.
Norbert Goertz, Johannes Gonter
VTC Spring1
2010 Joint Channel and Network Coding for Cooperative Diversity in a Shared-Relay Environment
abstract
In this paper we propose a cooperative diversity scheme for the communication model of two sources sharing a single relay. The scheme uses algebraic code superposition relaying in the multiple access fading channel to create spatial diversity under the constraint of limited communications resources. We also describe in detail a novel computationally efficient message passing algorithm at the destination's decoder which extracts the substantial spatial diversity contained in the code superposition and signal superposition. The decoder is based on a sliding window structure where certain a posteriori LLRs are retained to form a priori LLRs for the next decoding. We show that despite the simplicity of the proposed scheme, diversity gains are efficiently leveraged by the simple combination of channel coding at the sources and network coding at the relay.
Mark F. Flanagan, Norbert Goertz, John S. Thompson
IEEE Trans. Wirel. Commun.3
2009 Comments on the boundary of the capacity region of multiaccess fading channels
abstract
A modification is proposed for the formula known from the literature that characterizes the boundary of the capacity region of Gaussian multiaccess fading channels. The modified version takes into account potentially negative arguments of the cumulative distribution function that would affect the accuracy of the numerical capacity results.
Mohammad Shaqfeh, Norbert Goertz
IEEE Trans. Inf. Theory2
2009 Max-min relay selection for legacy amplify-and-forward systems with interference
abstract
In this paper, an amplify-and-forward (AF) cooperative strategy for interference limited networks is considered. In contrast to previously reported work, where the effect of interference is ignored, the effect of multi-user interference in AF schemes is analyzed. It is shown that the interference changes the statistical description of the conventional AF protocol and a statistical expression is subsequently derived. Asymptotic analysis of the expression shows that interference limits the diversity gain of the system and the related channel capacity is bounded by a stationary point. In addition, it is proven that previously proposed relay selection criteria for multi-relay scenarios become inefficient in the presence of interference. Based on consideration of the interference term, two extensions to the conventional max-min selection scheme suitable for different system setups are proposed. The extensions investigated are appropriate for legacy architectures with limitations on their flexibility where the max-min operation is pre-designed. A theoretical framework for selecting when to apply the proposed selection criteria is also presented. The algorithm investigated is based on some welldefined capacity approximations and incorporates the outage probabilities averaged over the fading statistics. Analytical results and simulation studies reveal enhancements of the proposed algorithm.
Ioannis Krikidis, John S. Thompson, Steve McLaughlin 0001, Norbert Goertz
IEEE Trans. Wirel. Commun.4
2008 Channel-Aware Scheduling with Resource-Sharing Constraints in Wireless Networks
abstract
In this paper, we consider the design of channel-aware scheduling policies for centralized wireless networks with resource-sharing constraints. The work is motivated by the objective to utilize the wireless system resources efficiently in addition to meeting the resource-sharing constraints. Our solutions are based on scheduling policies achieving close-to-capacity performance. We suggest two algorithms - an offline and an online solution - to properly adjust the weighting factors of the scheduling policy in order to achieve the required resource-sharing constraints.
Mohammad Shaqfeh, Norbert Goertz
ICC2
2008 Non-orthogonal Amplify-and-Forward for block-fading channels
abstract
In this paper, we deal with the amplify-and-forward (AF) cooperative strategy in slot-based block-fading environments. In contrast with previous schemes which assume a constant channel during the cooperative frame (several slots), here, we relax this constraint and assume a classical quasi-static block-fading channel (constant for one slot). This additional degree of freedom modifies the behavior of the conventional non-orthogonal (NAF) schemes and generates a new block-fading NAF (BFNAF) protocol where the source can usefully retransmit the same data during the cooperative slot. This new protocol is interesting at low spectral efficiencies where diversity against fading is more important. Another issue which is discussed throughout the paper is the optimal power allocation of the investigated schemes. The proposed power allocation strategy uses as an optimization criterion well-defined asymptotic expressions of the outage probabilities, averaged over the fading statistics.
Ioannis Krikidis, John S. Thompson, Steve McLaughlin 0001, Norbert Goertz
ISIT4
2008 Cross-Layer Issues for Cooperative Networks
abstract
This paper deals with a cross-layer approach for cooperative diversity networks which use a combination of Amplify-and-Forward (AF) and Decode-and-Forward (DF) as a relaying strategy. Based on a well-selected ad-hoc configuration, the proposed approach combines the AF diversity concept with a simultaneous optimization of Physical, Network and Multiple Access Control layers. The considered optimization problem requires an appropriate distribution of three roles among the network nodes which are the diversity-relays (AF concept), the intermediate-router (DF and routing) and the destination (scheduling). The proposed role assignment is based on the instantaneous channel conditions between the links and jointly supports performance optimization and a long-term fairness concept. In order to minimize the required complexity, a partial and quantized channel feedback is also proposed. The proposed cross-layer solution is compared with conventional approaches by computer simulations and theoretical studies, and we show that it achieves an efficient performance-complexity trade-off.
Ioannis Krikidis, John S. Thompson, Norbert Goertz
WCNC3
2007 On Bit Error Robustness of Trellis Source Codes
abstract
Trellis codes based on linear congruential recursions have recently been introduced as powerful source codes. For a modest computational complexity they offer excellent rate distortion performance at low to moderate quantization rates. In this work the bit error sensitivity of these codes is explored. The theoretical analysis shows that for a given number of trellis states the deviation from the correct trellis path, caused by bit errors on the transmission channel, can be described by two code parameters alone. The theoretic approach is compared to Monte-Carlo simulations and show that the particular trellis source codes under consideration offer robust transmission for bit error ratios up to the order of 10-3without the aid of any explicit correcting channel code.
Tomas Eriksson, Norbert Goertz
ICC2
2007 A Low-Complexity Path Metric for Tree-Based Multiple-Antenna Detectors
abstract
Traditional multiple-antenna detectors - which search a tree or a lattice structure - typically apply a metric that requires a preprocessing. Contrary to that, we present a straightforward solution for the metric that avoids those additional computations prior to the search. This new metric approach can even be used for the detection in under-determined systems with fewer receive than transmit antennas. Exemplarily, results are presented for turbo detection with the list-sequential (LISS) detector.
Christian Kuhn 0001, Norbert Goertz
ICC2
2007 Systematic Modification of Parity-Check Matrices for Efficient Encoding of LDPC Codes
abstract
An algorithm for efficient encoding of LDPC codes is presented that does not impose any restrictions on the construction of the parity-check matrices. The algorithm modifies the parity check matrix, without changing the subspace spanned by its rows, by removing linear dependent rows and adding a small number of new rows such that the graph-based message-passing encoder will not get stuck in a stopping set. The added rows are designed by a new algorithm which is based on the notion of the "key set". The encoder exploits the sparseness of the parity-check matrix, and the encoding complexity grows almost linear with the blocksize, because the number of added rows, which may not be sparse, is relatively small.
Mohammad Shaqfeh, Norbert Goertz
ICC2
2007 Linear Congruential Trellis Source Codes: Design and Analysis
abstract
Rate-distortion trellis source codes are developed for quantizing memoryless independent and identically distributed (i.i.d.) sources. The codes are generated by simple linear congruential recursions. The method generates codes at a variety of rates including fractional ones; reproducer sets can be large, a crucial advantage with certain sources. Axioms for good code construction are developed that are based on recursion properties and certain trellis symmetries. These axioms are justified by the outcome of random searches for good codes. It is found that the trellis code design breaks into two problems: the trellis labels should have certain properties regardless of the source distribution; and the reproducer values depend on the source. Encoders are simulated for a number of continuous amplitude sources. For the same computational complexity, the new codes, in most cases, perform better than the best codes in the literature, including trellis-coded quantization and fake process approaches.
Tomas Eriksson, John B. Anderson, Norbert Goertz
IEEE Trans. Commun.3
2007 On the BCJR Algorithm for Rate-Distortion Source Coding
abstract
The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is an important channel decoding method. We extend it to trellis rate-distortion data compression. Beginning from source coding principles, the derivation of the algorithm avoids channel coding or soft output ideas. The encoder does not use entropy coding; equiprobable reproducer letters are emphasized since these maximize entropy. The BCJR method is demonstrated by tests of a tail-biting variant. It performs much better than the ordinary Viterbi algorithm for short and medium blocks. However, the improvement stems from tail biting; the role of the BCJR is to achieve tail biting in a relatively simple way. Some issues that arise with tail biting are explored. It is shown that there is an optimal trellis state size for each block length.
John B. Anderson, Tomas Eriksson, Norbert Goertz
IEEE Trans. Inf. Theory3
2006 Trellis Based Variable Rate Residual Image Coding over Noisy Channels
abstract
We consider the lossy image compression problem and propose a model-residual approach. Polynomial basis images encode the model image and powerful new trellis codes quantize the residual part. A simple bit allocation scheme determines the residual bit rates and a variety of rates are attainable without entropy coding. The trellis structure is also used to form a joint source and channel coding scheme for the residual components. Results are shown for the 0.4-1.6 bits per pixel region. Comparisons are made to several state-of-the-art techniques and show that the proposed scheme is very competitive.
Tomas Eriksson, Norbert Goertz, Mirek Novak, John B. Anderson
DCC2
2006 Residual Image Coding Using Trellis Quantization
abstract
We consider the lossy image compression problem and propose a model-residual approach. Polynomial basis images encode the model image and powerful new trellis codes quantize the residual part. A simple bit allocation scheme determines the residual bit rates. Results are shown for the 0.4-1.6 bits per pixel region. Comparisons are made to several state-of-the-art techniques and show that the proposed scheme is very competitive
Tomas Eriksson, Norbert Goertz, Mirek Novak
ICASSP (2)2
2006 Logarithmic Bit-Significance Ratio: Definition, Calculation Rules and Examples
abstract
We motivate and discuss the logarithmic bit-significance ratio (S-value) which is a universal measure to quantify the significance of each bit in a digital communication system. Calculation rules for the S-values are given which, for instance, allow for the computation of the significances of parity bits when the significances of the data bits are given. The introduction of the S-value allows for the processing of soft-information, e.g., in encoding and modulation and can, hence, be interpreted as the transmitter-based counterpart of the well-established log-likelihood ratio (L-value) at the receiving end
Norbert Goertz, Tomas Eriksson, John B. Anderson
ISIT1
2005 On the BCJR algorithm for rate-distortion source coding
abstract
The BCJR algorithm is an important method of channel decoding. We extend it here to rate-distortion encoding. The arguments begin from source coding principles and make no use of channel coding or soft output ideas. An important role is played by codeword ensembles with equiprobable reproducer letters. The BCJR method is demonstrated by tests of a tailbiting BCJR with the Gaussian source. The outcome improves Viterbi algorithm performance at short and medium blocklengths
John B. Anderson, Norbert Goertz, Tomas Eriksson
ISIT2
2004 New Methods for Trellis Source Coding at Rates Above and Below One
abstract
This paper presents new methods trellis source coding at rates above and below one. The new schemes have in common a code design based on branch correlation, a large reproducer alphabet, and an encoder based on either the Viterbi algorithm or a tailbiting MAP technique. The methods are easily adapted to various bit rates, but here only the results for R = 2 and R = 1/2 bits per source sample are presented. Results, demonstrated for the memoryless Gaussian source, show similar or better performances than previous methods with similar coding complexity.
Tomas Eriksson, John B. Anderson, Mirek Novak, Norbert Goertz
Data Compression Conference4
2004 On iterative source-channel image decoding with Markov random field source models
abstract
In this paper, we propose a novel iterative source-channel decoding approach for robust transmission of compressed still images over noisy communication channels. Besides the explicit redundancy introduced by channel encoding, also implicit residual source redundancy is exploited for error protection. The source redundancy is modeled by a Markov random field (MRF) source model, which considers the residual spatial correlation after source encoding. The resulting MRF-based soft-input/soft-output source decoder is used as outer constituent decoder in the proposed iterative source-channel decoding scheme, where due to the link between MRFs and the Gibbs distribution, the source decoder can be implemented with very low complexity. We show that this iterative decoding scheme can be successfully employed for recovering the image data, especially when the channel is highly corrupted.
Jörg Kliewer, Norbert Goertz, Alfred Mertins
ICASSP (4)2
2003 Optimized symbol mappings for bit-interleaved coded modulation with iterative decoding
abstract
We investigate bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth efficient transmission, where the bit error rate is reduced through iterations between a multilevel demapper and a simple channel decoder. In order to achieve a significant turbo-gain, the assignment strategy of the binary indices to signal points is crucial. We address the problem of finding the most suitable index assignments to arbitrary, high order signal constellations. A new method based on the binary switching algorithm is proposed that finds optimized mappings outperforming previously known ones.
Frank Schreckenbach, Norbert Goertz, Joachim Hagenauer, Gerhard Bauch 0001
GLOBECOM2
2003 The turbo principle in joint source-channel coding
abstract
The turbo principle (iterative decoding between component decoders) is a general scheme, which we apply to joint source-channel decoding. As a realistic example (e.g., speech parameter coding), we discuss joint source-channel decoding for auto-correlated continuous-amplitude source samples. At the transmitter, the source samples are quantized and their indexes are appropriately mapped onto bitvectors. Afterwards, the bits are interleaved and channel-encoded; an AWGN channel is assumed for transmission. The auto-correlations of the source samples act as implicit outer channel codes that are serially concatenated with the inner explicit channel code. Thus, by applying the turbo principle, we can perform iterative decoding at the receiver. As an example, we show that, with a proper bit mapping for a 5-bit quantizer, iterative source-channel decoding saves up to 2 dB in channel SNR or 8 dB in source SNR for an auto-correlated Gaussian source.
Joachim Hagenauer, Norbert Goertz
ITW2
2003 Memory efficient adaptation of vector quantizers to time-varying channels
Norbert Goertz, Jörg Kliewer
Signal Process.1
2003 Optimization of the index assignments for multiple description vector quantizers
abstract
The optimization criterion and a practically feasible new algorithm is stated for the optimization of the index assignments of a multiple-description unconstrained vector quantizer with an arbitrary number of descriptions. In the simulations, the index-optimized multiple-description vector quantizer achieves significant gains in source signal-to-noise ratio over scalar multiple description schemes.
Norbert Goertz, Pornchai Leelapornchai
IEEE Trans. Commun.1
2002 Source-adaptive shifting of modulation signal points for improved transmission of waveform signals over noisy channels
abstract
A new algorithm is stated that uses source-adaptive shifting of modulation signals points for the improved transmission of waveform source signals over a noisy channel. A quantizer is used for source encoding and a non-binary digital modulation scheme for the transmission. The quantizer indexes are mapped to the points from the modulation signal constellation, but, in contrast to a conventional scheme, each transmitted signal point is shifted away from the one addressed by the quantizer index in order to reduce the source signal distortion at the receiver output. The shift is individually adapted to the each unquantized input source signal. A conventional receiver is used, i. e., the new algorithm requires only modifications at the transmitter. The simulation results show strong gains over a normal transmission scheme that does not apply source-adaptive shifting.
Norbert Goertz
ICASSP1
2002 AMR voice transmission over mobile internet
abstract
A very flexible transmission system for voice over mobile internet is proposed. With mobile internet a combination of a lossy packet-switched network and a wireless link of a mobile network is assumed. The new system allows to adaptively change the speech codec rate, and, thus, the payload of a packet, the number of transmitted packets and the number of used carriers on the mobile link depending on the packet error rate of the packet-switched network, and the downlink quality of the wireless link in a very flexible way. The proposed system is based on the Adaptive Multi-Rate (AMR) speech codec and a systematic convolutional code. Packeting of the speech data is done in such a way, that a packet-loss can be assumed as puncturing of the convolutional code. Thus, the only information that must be transmitted to the decoder is a bad frame indication, defining whether a certain packet out of the set of transmitted packets has been received or not. In a coding experiment the performance of the proposed system is analyzed and compared to a reference system using the G.711 codec. The proposed system outperforms the reference system over a wide range of signal to noise ratios of the wireless link and the packet error rates of the packet-switched network.
Markus Kaindl, Norbert Goertz
ICASSP2
2002 Iterative source-channel decoding for robust image transmission
abstract
In this paper we discuss the application of a joint source-channel decoding approach to image transmission over wireless channels. In addition to channel codes, also the implicit residual redundancy after source encoding in both horizontal and vertical direction is utilized for error protection. At the decoder we use an iterative (“turbo”) source-channel decoder which can be obtained in the same manner as for serially concatenated channel codes. As a new result we show that this iterative decoding scheme in combination with a novel simplified joint source and channel coding rate allocation at the encoder can be successfully employed for protecting the image data, especially when the channel is highly corrupted. Furthermore, when the source correlations are approximated with a large training set at the decoder, only a small loss in performance is observed.
Jörg Kliewer, Norbert Goertz
ICASSP2
2002 Turbo cross decoding of multiple descriptions
abstract
The transmission of multimedia data over best-effort packet networks has motivated a strong research effort in the area of multiple description coding. While most contributions concentrate on the design of encoders for the erasure channel, this paper considers the transmission of multiple descriptions over a typical wireless link. Assuming that channel state information is available and that the reliability of each transmitted bit is known to the receiver, we present a soft-in/soft-out decoder for a new class of block codes derived from multiple description scalar quantization. The idea of cross decoding multiple descriptions using soft information, can be successfully extended to the concatenation of multiple description codes and convolutional codes. For this case, the application of the turbo principle yields an iterative decoding scheme, which makes use of the correlation between descriptions in a very effective way.
João Ao Barros, Joachim Hagenauer, Norbert Goertz
ICC3
2001 Soft-input source decoding for robust transmission of compressed images using two-dimensional optimal estimation
abstract
We address the transmission of compressed images over highly corrupted AWGN-channels using an optimal estimation approach at the decoder. In contrast to other methods, we use only a negligible amount of explicit redundancy based on channel codes. Mainly, the implicit residual source redundancy inherent in the quantized subband images and the bit-reliability information at the channel output are utilized for error protection. As a novelty, we extend the optimal estimation technique from the one- to the two-dimensional case, where both horizontal and vertical correlations are exploited in the subband images. Based on this approach, the performances for several estimation methods are compared. Approaches for approximating the source correlations at the decoder are also discussed.
Jörg Kliewer, Norbert Goertz
ICASSP2
2001 On the iterative approximation of optimal joint source-channel decoding
abstract
Joint source-channel decoding is formulated as an estimation problem. The optimal solution is stated and it is shown that it is not feasible in many practical systems due to its complexity. Therefore, a novel iterative procedure for the approximation of the optimal solution is introduced, which is based on the principle of iterative decoding of turbo codes. New analytical expressions for different types of information in the optimal algorithm are used to derive the iterative approximation. A direct comparison of the performance of the optimal algorithm and its iterative approximation is given for a simple transmission system with "short" channel codewords. Furthermore, the performance of iterative joint source-channel decoding is investigated for a more realistic system.
Norbert Goertz
IEEE J. Sel. Areas Commun.1
1999 Joint source-channel decoding by channel-coded optimal estimation (CCOE) for a CELP speech codec
abstract
A model of intonation is trained here in order to capture stylistic factors for an application: reading of telephone directory listings. The system was designed to carry out one of the evaluation tasks of the 3rd International Workshop on Speech Synthesis in Jenolan-Australia and the input to the system conforms to the format of the listings defined there. The resulting synthetic prosody is fed into the ICP concatenative synthesis system and compared to natural prosody and prosody obtained from text reading material.
Norbert Goertz
EUROSPEECH1
1997 Zero-redundancy error protection for CELP speech codecs
Norbert Goertz
EUROSPEECH1