Joachim Rosenthal

Bio: Joachim Rosenthal is an academic researcher from University of Zurich. The author has contributed to research in topics: Convolutional code & Block code. The author has an hindex of 39, co-authored 246 publications receiving 4705 citations. Previous affiliations of Joachim Rosenthal include Arizona State University & École Polytechnique Fédérale de Lausanne.

Maximum Distance Separable Convolutional Codes

Abstract: A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of rate k/n. It is well known that MDS block codes do exist if the field size is more than n. In this paper we generalize this concept to the class of convolutional codes of a fixed rate k/n and a fixed code degree δ. In order to achieve this result we will introduce a natural upper bound for the free distance generalizing the Singleton bound. The main result of the paper shows that this upper bound can be achieved in all cases if one allows sufficiently many field elements.

Introduction to mathematical systems theory. a behavioral approach [Book Review]

Abstract: Traditionally, mathematical systems theory has been studied through an input–output framework. Kalman [8] taught us that an input–output system is best studied if one also includes state variables which, together with the input and output variables, describe the whole state of the system. This framework has been very successful and has built the foundation of mathematical systems theory up to this time. There are several excellent textbooks available covering linear and nonlinear systems theory from a mathematical point of view. Some of the most well known are [1], [4], [6], [7], [10], [14], and [18]. All these books approach systems theory through an input–state–output framework. Some people might even argue that input variables which can be freely chosen to influence the state and, hence, the output of a system are a distinctive feature of systems theory. The book under review makes a certain paradigm shift that has been initiated by the second author over the last two decades [15]–[17]. This approach de-emphasizes the input–output structure of a system and instead emphasizes the system behavior. The starting point is actually slightly more general than in the input–state–output framework. The basic object is a behavior B which is a subset of some universum (universe) . A mathematical model is an exclusion law that excludes from the universum all outcomes which are not part of the behavior. Input–output systems appear in this theory as a special instance. For this view the set of time trajectories lies inside the Cartesian product of the input-space and the output-space, which is the universum . Then define as the behavior the set of trajectories which can be generated by the input-output system. This shows that an input–output system describes a behavior. In the behavioral framework it is possible to naturally model situations where there is no immediate input and output structure. A good example consists of the motions of planets around the sun. The authors argue with right that a framework for mathematical systems theory should be capable of describing something as fundamental as Kepler’s law of planetary motions. Of course, there are countless other examples where there is no obvious signal flow direction and it is desirable to have a theory which can deal with general dynamical situations appearing in nature. For this purpose the book develops a theory of ordinary differential equations where in contrast to the classical situation [2] one has also ‘free variables’. In principle such a theory can be developed in a more general setting (nonlinear, stochastic and systems governed by PDE). The authors decide however to restrict their attention to systems governed by linear ordinary differential equations with constant coefficients. This makes the book accessible to a large audience and it makes it suitable as an advanced undergraduate text in applied mathematics. A student who has mastered the material of this text will be well prepared to study more advanced topics in systems and control theory.

Strongly-MDS convolutional codes

Abstract: Maximum-distance separable (MDS) convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper, a class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant. Such codes are called strongly-MDS convolutional codes. They also have a maximum or near-maximum distance profile. The extended row distances of these codes will also be discussed briefly.

Using low density parity check codes in the McEliece cryptosystem

Abstract: We examine the implications of using a low density parity check code (LDPCC) in place of the usual Goppa code in McEliece's cryptosystem. Using a LDPCC allows for larger block lengths and the possibility of a combined error correction/encryption protocol.

BCH convolutional codes

Abstract: Using a new parity-check matrix, a class of convolutional codes with a designed free distance is introduced. This new class of codes has many characteristics of BCH block codes, therefore, we call these codes BCH convolutional codes.

A cone complementarity linearization algorithm for static output-feedback and related problems

Abstract: This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with n/sub u/ (respectively, n/sub y/) independent inputs (respectively, outputs). The algorithm is based on a "cone complementarity" formulation of the problem and is guaranteed to produce a stabilizing controller of order m/spl les/n-max(n/sub u/,n/sub y/), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura's generic stabilizability result (m/spl les/n-n/sub u/-n/sub y/+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis.

Linear systems

Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

Abstract: This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical layer message authentication is also briefly introduced. The survey concludes with observations on potential research directions in this area.