Predicting private and public helping behaviour by implicit attitudes and the motivation to control prejudiced reactions

The role of individual differences in implicit attitudes toward homosexuals and motivation to control prejudiced reactions (MCPR) in predicting private and public helping behaviour was investigated. After assessing the predictor variables, 69 male students were informed about a campaign of a local gay organization. They were provided with an opportunity to donate money and sign a petition in the presence (public setting) or absence (private setting) of the experimenter. As expected, more helping behaviour was shown in the public than in the private setting. But while the explicit cognitive attitude accounted for helping behaviour in both settings, an implicit attitude x MCPR interaction accounted for additional variability of helping in the public setting only. Three different mediating processes are discussed as possible causes of the observed effects

Codes on Graphs and More

Modern communication systems strive to achieve reliable and efficient information transmission and storage with affordable complexity. Hence, efficient low-complexity channel codes providing low probabilities for erroneous receptions are needed. Interpreting codes as graphs and graphs as codes opens new perspectives for constructing such channel codes. Low-density parity-check (LDPC) codes are one of the most recent examples of codes defined on graphs, providing a better bit error probability than other block codes, given the same decoding complexity. After an introduction to coding theory, different graphical representations for channel codes are reviewed. Based on ideas from graph theory, new algorithms are introduced to iteratively search for LDPC block codes with large girth and to determine their minimum distance. In particular, new LDPC block codes of different rates and with girth up to 24 are presented. Woven convolutional codes are introduced as a generalization of graph-based codes and an asymptotic bound on their free distance, namely, the Costello lower bound, is proven. Moreover, promising examples of woven convolutional codes are given, including a rate 5/20 code with overall constraint length 67 and free distance 120. The remaining part of this dissertation focuses on basic properties of convolutional codes. First, a recurrent equation to determine a closed form expression of the exact decoding bit error probability for convolutional codes is presented. The obtained closed form expression is evaluated for various realizations of encoders, including rate 1/2 and 2/3 encoders, of as many as 16 states. Moreover, MacWilliams-type identities are revisited and a recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. Finally, the dissertation is concluded with exhaustive searches for convolutional codes of various rates with either optimum free distance or optimum distance profile, extending previously published results

Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems

This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We generalize the notion of projected dynamical systems to time-varying, possibly non-regular, domains and derive conditions for the existence of so-called Krasovskii solutions. The key insight is that for trajectories to exist, informally, the time-varying domain can only contract at a bounded rate whereas it may expand discontinuously. This condition is met, in particular, by feasible sets delimited via piecewise differentiable functions under appropriate constraint qualifications. To illustrate the necessity and usefulness of such a general framework, we consider a simple yet insightful power system example, and we discuss the implications of the proposed conditions for the design of feedback optimization schemes

Chained Gallager codes

The ensemble of regular Low-Density Parity-Check (LDPC) codes introduced by Gallager is considered. Using probabilistic arguments a lower bound on the normalized minimum distance is derived. A new code construction, called Chained Gallager codes, is introduced as the combination of two Gallager codes and its error correcting capabilities are studied

System Level Synthesis Beyond Finite Impulse Response Using Approximation by Simple Poles

Optimal linear feedback control design is valuable but challenging. The system level synthesis approach uses a reparameterization to expand the class of problems that can be solved using convex reformulations, among other benefits. However, to solve system level synthesis problems prior work relies on finite impulse response approximations that lead to deadbeat control, and that can experience infeasibility and increased suboptimality, especially in systems with large separation of time scales. This work develops a new technique by combining system level synthesis with a new approximation based on simple poles. The result is a new design method which does not result in deadbeat control, is convex and tractable, always feasible, can incorporate prior knowledge, and works well for systems with large separation of time scales. A general suboptimality result is provided which bounds the approximation error based on the geometry of the pole selection. The bound is then specialized to a particularly interesting pole selection to obtain a non-asymptotic convergence rate. An example demonstrates superior performance of the method.Comment: 25 page

Another look at the exact bit error probability for Viterbi decoding of convolutional codes

In 1995, Best et al. published a formula for the exact bit error probability for Viterbi decoding of the rate R=1/2, memory m=1 (2-state) convolutional encoder with generator matrix G(D)=(1 1+D) when used to communicate over the binary symmetric channel. Their method was later extended to the rate R=1/2, memory m=2 (4-state) generator matrix G(D)=(1+D^2 1+D+D^2) by Lentmaier et al. In this paper, we shall use a different approach to derive the exact bit error probability. We derive and solve a general matrix recurrent equation connecting the average information weights at the current and previous steps of the Viterbi decoding. A closed form expression for the exact bit error probability is given. Our general solution yields the expressions for the exact bit error probability obtained by Best et al. (m=1) and Lentmaier et al. (m=2) as special cases. The exact bit error probability for the binary symmetric channel is determined for various 8 and 16 states encoders including both polynomial and rational generator matrices for rates R=1/2 and R=2/3. Finally, the exact bit error probability is calculated for communication over the quantized additive white Gaussian noise channel

Searching for high-rate convolutional codes via binary syndrome trellises

Rate R=(c-1)/c convolutional codes of constraint length nu can be represented by conventional syndrome trellises with a state complexity of s=nu or by binary syndrome trellises with a state complexity of s=nu or s=nu+1, which corresponds to at most 2^s states at each trellis level. It is shown that if the parity-check polynomials fulfill certain conditions, there exist binary syndrome trellises with optimum state complexity s=nu. The BEAST is modified to handle parity-check matrices and used to generate code tables for optimum free distance rate R=(c-1)/c, c=3,4,5, convolutional codes for conventional syndrome trellises and binary syndrome trellises with optimum state complexity. These results show that the loss in distance properties due to the optimum state complexity restriction for binary trellises is typically negligible

A rate R=5/20 hypergraph-based woven convolutional code with free distance 120

A rate R=5/20 hypergraph-based woven convolu- tional code with overall constraint length 67 and constituent con- volutional codes is presented. It is based on a 3-partite, 3-uniform, 4-regular hypergraph and contains rate R=3/4 constituent convolutional codes with overall constraint length 5. Although the code construction is based on low-complexity codes, the free distance of this construction, computed with the BEAST algorithm, is dfree=120, which is remarkably large

Double-Hamming based QC LDPC codes with large minimum distance

A new method using Hamming codes to construct base matrices of (J, K)-regular LDPC convolutional codes with large free distance is presented. By proper labeling the corresponding base matrices and tailbiting these parent convolutional codes to given lengths, a large set of quasi-cyclic (QC) (J, K)-regular LDPC block codes with large minimum distance is obtained. The corresponding Tanner graphs have girth up to 14. This new construction is compared with two previously known constructions of QC (J, K)-regular LDPC block codes with large minimum distance exceeding (J+1)!. Applying all three constructions, new QC (J, K)-regular block LDPC codes with J=3 or 4, shorter codeword lengths and/or better distance properties than those of previously known codes are presented