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Margreta Kuijper

Publications and source records attributed to Margreta Kuijper.

At least 19 recordsLinked to original sources
arXiv2026

On Unified and Sharpened CMI Bounds for Generalization Errors

We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$ denoting the number of the hold-out supersamples. Under this setting, we propose a unified CMI-based bound, allowing to envelop and reproduce many known CMI-based bounds and also bridge the gap between the MI- and CMI-based bounds when $m$ tends to infinity. The proposed framework not only provides a unified description of the existing bounds but also develops new, sharper bounds. We show the benefits of the proposed bounds through several simple examples, where the existing results are either inapplicable or looser. Moreover, under the premise that the loss function is bounded, we tighten the CMI quantities involved in the proposed bounds by reducing the number of conditional terms, thereby enhancing the proposed framework. We show empirically that the resulting new bounds improve upon the previously known ones.

cs.IT↗
arXiv2025

Easy repair via codes with simplex locality

In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements, measured by the code's rate, minimum distance, locality, availability as well as field size, influence each other and can not all be maximized at the same time. We focus on the notion of easy repair, more specifically on the construction of codes that can repair correctable erasure patterns with minimal computational effort. In particular, we introduce the easy repair property and then present codes of different rates that possess this property. The presented codes are all in some way related to simplex codes and comprise block codes as well as unit-memory convolutional codes. We also formulate conditions under which the easy repairs can be performed in parallel, thus improving access speed of the distributed storage system.

cs.IT↗
arXiv2024

Lightweight Conceptual Dictionary Learning for Text Classification Using Information Compression

We propose a novel, lightweight supervised dictionary learning framework for text classification based on data compression and representation. This two-phase algorithm initially employs the Lempel-Ziv-Welch (LZW) algorithm to construct a dictionary from text datasets, focusing on the conceptual significance of dictionary elements. Subsequently, dictionaries are refined considering label data, optimizing dictionary atoms to enhance discriminative power based on mutual information and class distribution. This process generates discriminative numerical representations, facilitating the training of simple classifiers such as SVMs and neural networks. We evaluate our algorithm's information-theoretic performance using information bottleneck principles and introduce the information plane area rank (IPAR) as a novel metric to quantify the information-theoretic performance. Tested on six benchmark text datasets, our algorithm competes closely with top models, especially in limited-vocabulary contexts, using significantly fewer parameters. \review{Our algorithm closely matches top-performing models, deviating by only ~2\% on limited-vocabulary datasets, using just 10\% of their parameters. However, it falls short on diverse-vocabulary datasets, likely due to the LZW algorithm's constraints with low-repetition data. This contrast highlights its efficiency and limitations across different dataset types.

cs.CL↗
arXiv2019

A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

We address the problem of state estimation and attack isolation for general discrete-time nonlinear systems when sensors are corrupted by (potentially unbounded) attack signals. For a large class of nonlinear plants and observers, we provide a general estimation scheme, built around the idea of sensor redundancy and multi-observer, capable of reconstructing the system state in spite of sensor attacks and noise. This scheme has been proposed by others for linear systems/observers and here we propose a unifying framework for a much larger class of nonlinear systems/observers. Using the proposed estimator, we provide an isolation algorithm to pinpoint attacks on sensors during sliding time windows. Simulation results are presented to illustrate the performance of our tools.

eess.SY↗
arXiv2019

An Unknown Input Multi-Observer Approach for Estimation and Control under Adversarial Attacks

We address the problem of state estimation, attack isolation, and control of discrete-time linear time-invariant systems under (potentially unbounded) actuator and sensor false data injection attacks. Using a bank of unknown input observers, each observer leading to an exponentially stable estimation error (in the attack-free case), we propose an observer-based estimator that provides exponential estimates of the system state in spite of actuator and sensor attacks. Exploiting sensor and actuator redundancy, the estimation scheme is guaranteed to work if a sufficiently small subset of sensors and actuators are under attack. Using the proposed estimator, we provide tools for reconstructing and isolating actuator and sensor attacks; and a control scheme capable of stabilizing the closed-loop dynamics by switching off isolated actuators. Simulation results are presented to illustrate the performance of our tools.

eess.SY↗
arXiv2018

An Unknown Input Multi-Observer Approach for Estimation, Attack Isolation, and Control of LTI Systems under Actuator Attacks

We address the problem of state estimation, attack isolation, and control for discrete-time Linear Time Invariant (LTI) systems under (potentially unbounded) actuator false data injection attacks. Using a bank of Unknown Input Observers (UIOs), each observer leading to an exponentially stable estimation error in the attack-free case, we propose an estimator that provides exponential estimates of the system state and the attack signals when a sufficiently small number of actuators are attacked. We use these estimates to control the system and isolate actuator attacks. Simulations results are presented to illustrate the performance of the results.

eess.SY↗
arXiv2018

A Multi-Observer Approach for Attack Detection and Isolation of Discrete-Time Nonlinear Systems

We address the problem of attack detection and isolation for a class of discrete-time nonlinear systems under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose two algorithms for detecting and isolating sensor attacks. These algorithms make use of the ISS property of the observers to check whether the trajectories of observers are `consistent' with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the proposed algorithms.

eess.SY↗
arXiv2018

A Robust Circle-criterion Observer-based Estimator for Discrete-time Nonlinear Systems in the Presence of Sensor Attacks and Measurement Noise

We address the problem of robust state estimation of a class of discrete-time nonlinear systems with positive-slope nonlinearities when the sensors are corrupted by (potentially unbounded) attack signals and bounded measurement noise. We propose an observer-based estimator, using a bank of circle-criterion observers, which provides a robust estimate of the system state in spite of sensor attacks and measurement noise. We first consider the attack-free case where there is measurement noise and we provide a design method for a robust circle-criterion observer. Then, we consider the case when a sufficiently small subset of sensors are subject to attacks and all sensors are affected by measurement noise. We use our robust circle-criterion observer as the main ingredient in building an estimator that provides robust state estimation in this case. Finally, we propose an algorithm for isolating attacked sensors in the case of bounded measurement noise. We test this algorithm through simulations.

eess.SP↗
arXiv2017

Linear system security -- detection and correction of adversarial attacks in the noise-free case

We address the problem of attack detection and attack correction for multi-output discrete-time linear time-invariant systems under sensor attack. More specifically, we focus on the situation where adversarial attack signals are added to some of the system's output signals. A 'security index' is defined to characterize the vulnerability of a system against such sensor attacks. Methods to compute the security index are presented as are algorithms to detect and correct for sensor attacks. The results are illustrated by examples involving multiple sensors.

eess.SP↗
arXiv2015

Gabidulin Decoding via Minimal Bases of Linearized Polynomial Modules

We show how Gabidulin codes can be decoded via parametrization by using interpolation modules over the ring of linearized polynomials with composition. Our decoding algorithm computes a list of message words that correspond to all closest codewords to a given received word. This involves the computation of a minimal basis for the interpolation module that corresponds to the received word, followed by a search through the parametrization for valid message words. Our module-theoretic approach strengthens the link between Gabidulin decoding and Reed-Solomon decoding. Two subalgorithms are presented to compute the minimal basis, one iterative, the other an extended Euclidean algorithm. Both of these subalgorithms have polynomial time complexity. The complexity order of the overall algorithm, using the parametrization, is then compared to straightforward exhaustive search as well as to chase list decoding.

cs.IT↗
arXiv2014

Iterative List-Decoding of Gabidulin Codes via Gröbner Based Interpolation

We show how Gabidulin codes can be list decoded by using an iterative parametrization approach. For a given received word, our decoding algorithm processes its entries one by one, constructing four polynomials at each step. This then yields a parametrization of interpolating solutions for the data so far. From the final result a list of all codewords that are closest to the received word with respect to the rank metric is obtained.

cs.IT↗
arXiv2014

List-Decoding Gabidulin Codes via Interpolation and the Euclidean Algorithm

We show how Gabidulin codes can be list decoded by using a parametrization approach. For this we consider a certain module in the ring of linearized polynomials and find a minimal basis for this module using the Euclidean algorithm with respect to composition of polynomials. For a given received word, our decoding algorithm computes a list of all codewords that are closest to the received word with respect to the rank metric.

cs.IT↗
arXiv2014

Erasure codes with simplex locality

We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms of the generator matrix of the code. These lead to bounds on locality and notions of optimality. We then examine the locality properties of a family of non-binary codes with simplex structure. We investigate their optimality and design several easy repair decoding methods. In particular, we show that any correctable erasure pattern can be solved by easy repair.

cs.IT↗
arXiv2011

An algebraic approach to source coding with side information using list decoding

Existing literature on source coding with side information (SCSI) mostly uses the state-of-the-art channel codes namely LDPC codes, turbo codes, and their variants and assume classical unique decoding. In this paper, we present an algebraic approach to SCSI based on the list decoding of the underlying channel codes. We show that the theoretical limit of SCSI can be achieved in the proposed list decoding based framework when the correlation between the source and side information is $q$-ary symmetric. We argue that, as opposed to channel coding, the correct sequence from the list produced by the list decoder can effectively be recovered in case of SCSI with a few CRC symbols. The CRC symbols, which allow the decoder to identify the correct sequence, incur negligible overhead for large block lengths. More importantly, these CRC symbols are not subject to noise since we are dealing with a virtual noisy channel rather than a real noisy channel. Finally, we present a guideline for designing constructive SCSI schemes for non-binary and binary sources using Reed Solomon codes and BCH codes, respectively. This guideline allows us to design a SCSI scheme for any arbitrary $q$-ary symmetric correlation without resorting to simulation.

cs.IT↗
arXiv2011

A parametric approach to list decoding of Reed-Solomon codes using interpolation

In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Minimal list decoding for a code $C$ refers to list decoding with radius $L$, where $L$ is the minimum of the distances between the received word $\mathbf{r}$ and any codeword in $C$. We consider the problem of determining the value of $L$ as well as determining all the codewords at distance $L$. Our approach involves a parametrization of interpolating polynomials of a minimal Gröbner basis $G$. We present two efficient ways to compute $G$. We also show that so-called re-encoding can be used to further reduce the complexity. We then demonstrate how our parametric approach can be solved by a computationally feasible rational curve fitting solution from a recent paper by Wu. Besides, we present an algorithm to compute the minimum multiplicity as well as the optimal values of the parameters associated with this multiplicity which results in overall savings in both memory and computation.

cs.IT↗
arXiv2010

Source Coding With Side Information Using List Decoding

The problem of source coding with side information (SCSI) is closely related to channel coding. Therefore, existing literature focuses on using the most successful channel codes namely, LDPC codes, turbo codes, and their variants, to solve this problem assuming classical unique decoding of the underlying channel code. In this paper, in contrast to classical decoding, we have taken the list decoding approach. We show that syndrome source coding using list decoding can achieve the theoretical limit. We argue that, as opposed to channel coding, the correct sequence from the list produced by the list decoder can effectively be recovered in case of SCSI, since we are dealing with a virtual noisy channel rather than a real noisy channel. Finally, we present a guideline for designing constructive SCSI schemes using Reed Solomon code, BCH code, and Reed-Muller code, which are the known list-decodable codes.

cs.IT↗