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Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June 2017 ; Jalali and Poor ("Universal compressed sensing," arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of Rényi's information dimension to stationary stochastic processes by defining the information dimension of the stochastic process as the information dimension of k samples divided by k in the limit as k →∞ to. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m →∞ ; to. It is demonstrated that both definitions are equivalent for stochastic processes that are ψ*-mixing, but that they may differ in general. In particular, it is shown that for Gaussian processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is 1 if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size. ; The work of Bernhard C. Geiger has been funded by the Erwin Schrödinger Fellowship J 3765 of the Austrian Science Fund and by the German Ministry of Education and Research in the framework of an Alexander von Humboldt Professorship. The work of Tobias Koch has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013- 41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845.

In dem vorliegenden Beitrag werden exemplarisch anhand der Daten des australischen Household, Income and Labor Dynamics in Australia Surveys 10 (HILDA 10) einige basale Multilevelmodelle für längsschnittliche Daten vorgestellt. Hierbei handelt es sich um Übertragungen des Random-Intercept-Only-Modells, des Random-Intercept-Modells und des Random-Intercept-Random-Slope-Modells mit Level-1- und Level-2-Prädiktoren auf längsschnittliche Daten. Es wird auf die Modellierung von Kontexteffekten eingegangen. Eine Besonderheit bei längsschnittlichen Daten liegt darin, dass der Kontext der zeitvariierenden Beobachtungen auf Ebene-1 die Person (Ebene-2) darstellt. Um Effekte der soziologischen Makro-Ebene zu berücksichtigen, ist es notwendig, die Modelle um eine dritte Ebene zu erweitern. Ein Modell mit drei Ebenen wird vorgestellt und weitere Modelle zur Modellierung von Daten im Längsschnitt, wie ein Wachstumskurvenmodell und ein multivariates Multilevelmodell, werden kurz behandelt.

This article concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals $L$ over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more. ; The work of A. Lancho and T. Koch was supported in part by the Spanish Ministerio de Economia y Competitividad under Grant TEC2013-41718-R and Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU), in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under Grant 714161, and in part by the Comunidad de Madrid under Grant S2103/ICE-2845. The work of A. Lancho further was supported by an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274. The work of T. Koch further was supported in part by the Spanish Ministerio de Economía y Competitividad under Grant RYC-2014-16332 and in part by the 7th European Union Framework Programme under Grant 333680. The work of G. Durisi was supported by the Swedish Research Council under Grant 2012-4571 and Grant 2016-03293.

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely, Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and maximum likelihood (ML) decoding at GC nodes into our analysis without resorting on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity, but the optimal fraction is strictly smaller than one. We then consider techniques to further reduce the gap to capacity by means of random puncturing, and the inclusion of a certain fraction of generalized variable nodes in the graph. ; This work was supported in part by the Spanish Ministerio de Economía y Competitividad and the Agencia Española de Investigación under Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU) and in part by the Comunidad de Madrid in Spain under Grant S2103/ICE-2845, Grant IND2017/TIC-7618, Grant IND2018/TIC-9649, and Grant Y2018/TCS-4705. P. M. Olmos was further supported by the Spanish Ministerio de Economía y Competitividad under Grant IJCI-2014-19150. T. Koch was further supported by the European Research Council (ERC) through the European Union's Horizon 2020 research and innovation programme under Grant 714161, by the 7th European Union Framework Programme under Grant 333680, and by the Spanish Ministerio de Economía y Competitividad under Grant TEC2013- 41718-R and Grant RYC-2014-16332.

Proceeding of: 52nd Annual Conference on Information Sciences and Systems (CISS 2018) ; Capacity and outage capacity characterize the maximum coding rate at which reliable communication is feasible when there are no constraints on the packet length. Evaluated for fading channels, they are important performance benchmarks for wireless communication systems. However, the latency of a communication system is proportional to the length of the packets it exchanges, so assuming that there are no constraints on the packet length may be overly optimistic for communication systems with stringent latency constraints. Recently, there has been great interest within the information theory community in characterizing the maximum coding rate for short packet lengths. Research on this topic is often concerned with asymptotic expansions of the coding rate with respect to the packet length, which then give rise to normal approximations. In this paper, we review existing normal approximations for single-antenna Rayleigh block-fading channels and compare them with the high-SNR normal approximation we presented at the 2017 IEEE International Symposium on Information Theory (Lancho, Koch, and Durisi, 2017). We further discuss how these normal approx- imations may help to assess the performance of communication protocols. ; A. Lancho and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), from an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274, and from the Comunidad de Madrid under Grant S2103/ICE-2845. G. Durisi has been supported by the Swedish Research Council under Grant and 2016-03293.

Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017 ; In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without having to resort on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoder (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a success probability that depends on the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code. We illustrate our analysis for GLDPC code ensembles using (2, 6) and (2,15) base DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity. ; This work has been funded in part by the Spanish Ministerio de Economía y Competitividad and the Agencia Española de Investigación under Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU) and by the Comunidad de Madrid in Spain under Grant S2103/ICE-2845. T. Koch has further received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, and from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R and RYC-2014-16332. Pablo M. Olmos has further received funding from the Spanish Ministerio de Economía y Competitividad under Grant IJCI-2014-19150.

Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017 ; This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB. ; A. Lancho and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), from an FPU fellowship from the Spanish Ministerio de Educación, Cultura y Deporte under Grant FPU14/01274 and from the Comunidad de Madrid under Grant S2103/ICE-2845. G. Durisi has been supported by the Swedish Research Council under Grants 2012-4571 and 2016-03293.

c.t. stellt eine »Revolution« in der Methode juristischen Lernens dar: Kollaborative Elemente werden auf innovative Weise in herkömmliches E-Learning integriert. -- Studierende schreiben Klausuren nicht mehr jeder für sich, sondern arbeiten im Teamverbund auf einer virtuellen Plattform in Echtzeit unter tutorieller Begleitung an der Falllösung. Danach korrigieren sie wiederum im Team die Klausuren der Kommilitonen. Dabei lernen sie voneinander, profitieren von den Stärken und Schwächen der Anderen und lernen ihre eigenen Stärken und Schwächen kennen. Das Wissen der einzelnen Teilnehmer wird dadurch gebündelt und potenziert, so dass die Qualität der Lösung durch die entstandenen Synergieeffekte eine neue Qualitätsstufe erreicht. -- Das vorliegende Werk unterzieht die sich bei c.t. aufdrängenden Rechtsfragen einer umfassenden rechtlichen Würdigung. Nach einer allgemeinen Einführung in das E-Learning stellen datenschutz- und urheberrechtliche Fragen sowie die Problemstellungen des IT-Sicherheitsrechts den Schwerpunkt der Begutachtung dar

This paper investigates the maximal achievable rate for a given blocklength and error probability over quasi-static multiple-input multiple-output fading channels, with and without channel state information at the transmitter and/or the receiver. The principal finding is that outage capacity, despite being an asymptotic quantity, is a sharp proxy for the finite-blocklength fundamental limits of slow-fading channels. Specifically, the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver, at only one of them, or at neither of them. These results follow from analytically tractable converse and achievability bounds. Numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases. In the example of a particular 1 × 2 single-input multiple-output Rician fading channel, the blocklength required to achieve 90% of capacity is about an order of magnitude smaller compared with the blocklength required for an AWGN channel with the same capacity. For this specific scenario, the coding/decoding schemes adopted in the LTE-Advanced standard are benchmarked against the finite-blocklength achievability and converse bounds. ; Swedish Research Council (Grant 2012-4571) ; Ericsson Research Foundation (Grant FOSTIFT-12:022) ; European Union (Framework Programme, Marie Curie FP7 Integration Grant 333680) ; Spain (Grant TEC2009-14504-C02-01) ; Spain (Grant CSD2008- 00010) ; Spain (Grant TEC2012-38800-C03-01) ; National Science Foundation (U.S.) (Grant CCF-1253205)