Efficient FPGA Realization of CORDIC With Application to Robotic Exploration

We present an area-efficient method and field-programmable gate array (FPGA) realization for two common operations in robotics, namely, the following: 1) rotating a vector in 2-D and 2) aligning a vector in the plane with a specific axis. It is based on a new coordinate rotation digital computer (CORDIC) algorithm that is designed to work with a small set of elementary angles. Unlike conventional CORDIC, the proposed algorithm does not require a ROM and a full-fledged barrel shifter. The proposed CORDIC algorithm is used to design hardware-efficient solutions for two mobile robotic tasks in an indoor environment without employing division and floating-point calculations. Experiments with a sole low-end FPGA-based robot in static as well as dynamic environments validate the power of the approach.      

Universal Lossless Compression of Erased Symbols

A source ${mmb X}$ goes through an erasure channel whose output is ${mmb Z}$. The goal is to compress losslessly ${mmb X}$ when the compressor knows ${mmb X}$ and ${mmb Z}$ and the decompressor knows ${mmb Z}$. We propose a universal algorithm based on context-tree weighting (CTW), parameterized by a memory-length parameter $ell$. We show that if the erasure channel is stationary and memoryless, and ${mmb X}$ is stationary and ergodic, then the proposed algorithm achieves a compression rate of $H(X_0vert X_{-ell}^{-1}, Z^ell)$ bits per erasure.      

Properties and Applications of Preimage Distributions of Perfect Nonlinear Functions

The preimage distributions of perfect nonlinear functions from an Abelian group of order $n$ to an Abelian group of order $3$ or $4$, respectively, are studied. Based on the properties of the preimage distributions of perfect nonlinear functions from an Abelian group of order $3^{r}$ to an Abelian group of order $3$, the weight distributions of the ternary linear codes $C_{Pi}$ from the perfect nonlinear functions $Pi (x)$ from $F_{3^{r}}$ to itself are determined. These results suggest that two open problems, proposed by Carlet, Ding, and Yuan in 2005 and 2006, respectively, are answered.      

High-Temperature High-Power Operation of GaInNAs Laser Diodes in the 1220–1240-nm Wavelength Range

We report on the high-temperature performance of high-power GaInNAs broad area laser diodes with different waveguide designs emitting in the 1220–1240-nm wavelength range. Large optical cavity laser structures enable a maximum continuous-wave output power of $>$8.9 W at ${T}=20 ^{circ}$C with emission at 1220 nm and are characterized by low internal losses of 0.5 cm$^{-1}$ compared to 2.9 cm$^{-1}$ for the conventional waveguide structures. High-power operation up to temperatures of 120 $^{circ}$C is observed with output powers of $>$4 W at ${T}=90 ^{circ}$C. This laser diode showed characteristic temperatures of ${T}_{0} =112$ K and ${T}_{1}=378$ K.      

On the Values of Kloosterman Sums

Given a prime $p$ and a positive integer $n$ , we show that the shifted Kloosterman sums $$sum _{x in BBF _{p^{n}}} psi (x + ax^{p^{n}-2}) = sum _{xin BBF _{p^{n}}^{ast }} psi(x + ax^{-1}) + 1, quad a inBBF _{p^{n}}^{ast }$$ where $psi$ is a nontrivial additive character of a finite field $BBF _{p^{n}}$ of $p^{n}$ elements, do not vanish if $a$ belongs to a small subfield $BBF_{p^{m}} subseteq BBF _{p^{n}}$. This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions.      

Managing Information Technology Project Escalation and De-Escalation: An Approach-Avoidance Perspective

This paper presents an integrated theoretical process model for identifying , describing, and analyzing the complex escalation and de-escalation phenomena in software development projects. The approach-avoidance theory is used to integrate core elements of various escalation theories into a holistic, explanatory framework for the two phenomena. We use a process model to identify antecedent conditions, sequences of events, critical incidents, and outcomes over the course of a project. The analysis also operates at multiple levels: project, work, and environment. This highlights the recursive interactions between project, organizational work activities, and their contexts during the software project development process. By conceiving the processes of commitment escalation and de-escalation as sequences of events involving recurring approach-avoidance decision conflict, this research allows for a deeper understanding of the ambiguity and dilemma that decision makers face during project escalations and de-escalations. Our proposed model was both informed by a detailed case study that exhibits both project escalation and de-escalation conditions, and at the same time, illuminates the perspectives of various stakeholders.      

Sharp $p$ -Divisibility of Weights in Abelian Codes Over ${BBZ}/p^d{BBZ}$

A theorem of McEliece on the $p$-divisibility of Hamming weights in cyclic codes over ${BBF}_p$ is generalized to Abelian codes over ${{{BBZ}/p^d{BBZ}}}$. This work improves upon results of Helleseth–Kumar–Moreno–Shanbhag, Calderbank–Li–Poonen, Wilson, and Katz. These previous attempts are not sharp in general, i.e., do not report the full extent of the $p$ -divisibility except in special cases, nor do they give accounts of the precise circumstances under which they do provide best possible results. This paper provides sharp results on $p$-divisibilities of Hamming weights and counts of any particular symbol for an arbitrary Abelian code over ${{{BBZ}/p^d{BBZ}}}$. It also presents sharp results on $2$-divisibilities of Lee and Euclidean weights for Abelian codes over ${{{BBZ}/4{BBZ}}}$.      

Single-Exclusion Number and the Stopping Redundancy of MDS Codes

For a linear block code ${cal C}$, its stopping redundancy is defined as the smallest number of check nodes in a Tanner graph for ${cal C}$, such that there exist no stopping sets of size smaller than the minimum distance of ${cal C}{bf .},$ Schwartz and Vardy conjectured that the stopping redundancy of a maximum-distance separable (MDS) code should only depend on its length and minimum distance.      

Logarithmic Sobolev Inequalities for Information Measures

For $alphageq 1$, the new Vajda-type information measure ${bf J}_{alpha}(X)$ is a quantity generalizing Fisher's information (FI), to which it is reduced for $alpha=2$ . In this paper, a corresponding generalized entropy power ${bf N}_{alpha}(X)$ is introduced, and the inequality ${bf N}_{alpha}(X) {bf J}_{alpha}(X)geq n$ is proved, which is reduced to the well-known inequality of Stam for $alpha=2$. The cases of equality are also determined. Furthermore, the Blachman–Stam inequality for the FI of convolutions is generalized for the Vajda information ${bf J}_{alpha}(X)$ and both families of results in the context of measure of information are discussed. That is, logarithmic Sobolev inequalities (LSIs) are written in terms of new more general entropy-type information measure, and therefore, new information inequalities are arisen. This generalization for special cases yields to the well known information measures and relative bounds.      

On the Cusick–Cheon Conjecture About Balanced Boolean Functions in the Cosets of the Binary Reed–Muller Code

In this paper, an amplification of the Cusick–Cheon conjecture on balanced Boolean functions in the cosets of the binary Reed–Muller code $RM(k,m)$ of order $k$ and length $2^m$, in the cases where $k = 1$ or $k geq (m-1)/2$, is proved.      

Robust Precoder Adaptation for MIMO Links With Noisy Limited Feedback

In this paper, we propose two robust limited feedback designs for multiple-input multiple-output (MIMO) adaptation. The first scheme, namely, the combined design jointly optimizes the adaptation, CSIT (channel state information at the transmitter) feedback as well as index assignment strategies. The second scheme, namely, the decoupled design, focuses on the index assignment problem given an error-free limited feedback design. Simulation results show that the proposed framework has significant capacity gain compared to the naive design (designed assuming there is no feedback error). Furthermore, for large number of feedback bits $C_{rm fb}$, we show that under two-nearest constellation feedback channel assumption, the MIMO capacity loss (due to noisy feedback) of the proposed robust design scales like ${cal O}(P_e2^{-{{C_{rm fb}}over{t+1}}})$ for some positive integer $t$. Hence, the penalty due to noisy limited feedback in the proposed robust design approaches zero as $C_{rm fb}$ increases.      

Lattices for Distributed Source Coding: Jointly Gaussian Sources and Reconstruction of a Linear Function

Consider a pair of correlated Gaussian sources $(X_1,X_2)$. Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear combination of $X_1$ and $X_2$ to within a mean-square distortion of $D$. We obtain an inner bound to the optimal rate–distortion region for this problem. A portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components $X_1$ and $X_2$ first. This results in a better rate region for certain parameter values. Our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory. We then consider the case of linear reconstruction of $K$ sources and provide an inner bound to the optimal rate–distortion region. Some parts of the inner bound are achieved using the following coding structure: lattice vector quantization followed by “correlated” lattice-structured binning.      

Explicit Model-Predictive Control of a PWM Inverter With an LCL Filter

This paper deals with the control of pulsewidth modulation inverters connected to the grid through resonant LCL filters. It proposes two alternative (piecewise affine) models that account for the switched behavior of the converter. Based on these improved models, an explicit model-predictive control scheme is derived in order to provide a fast response, making it very suitable for applications, such as active filtering, where a large bandwidth is required. A state observer and a grid voltage estimator are used in order to reduce the number of required sensors and to eliminate noise. The control scheme relies only on filtered current measurements and on the dc voltage.      

Universal FIR MMSE Filtering

We consider the problem of causal estimation, i.e., filtering, of a real-valued signal corrupted by zero mean, time-independent, real-valued additive noise, under the mean-squared error (MSE) criterion. We build a universal filter whose per-symbol squared error, for every bounded underlying signal, is essentially as small as that of the best finite-duration impulse response (FIR) filter of a given order. We do not assume a stochastic mechanism generating the underlying signal, and assume only that the variance of the noise is known to the filter. The regret of the expected MSE of our scheme is shown to decay as $O(log n/n)$, where $n$ is the length of the signal. Moreover, we present a stronger concentration result which guarantees the performance of our scheme not only in expectation, but also with high probability. Our result implies a conventional stochastic setting result, i.e., when the underlying signal is a stationary process, our filter achieves the performance of the optimal FIR filter. We back our theoretical findings with several experiments showcasing the potential merits of our universal filter in practice. Our analysis combines tools from the problems of universal filtering and competitive on-line regression.      

Performance Analysis and Design Criteria of BICM-ID With Signal Space Diversity for Keyhole Nakagami-$m$ Fading Channels

This paper generalizes the application bit-interleaved coded modulation with iterative decoding (BICM-ID) using signal space diversity (SSD) over keyhole Nakagami-$m$ fading channels. The tight union bound on the asymptotic error performance is first analytically derived. The near-optimal rotation matrix with respect to both the asymptotic performance and the convergence behavior is then determined. In particular, it is demonstrated that the suitable rotation matrix is the one that has 1) all entries equal in magnitude, 2) a high diversity order, and 3) a large minimum product of the ratios between squared distances to the power $m$ and log-squared distances to the power $m$ of the rotated constellation scaled by factors of signal-to-noise ratio (SNR) and the parameter $m$ . Various analytical and simulation results show that by employing SSD with a sufficiently large dimension, the error performance can closely approach that over an additive white Gaussian noise (AWGN) channel, even in the worst case of keyhole fading.      

On the Achievable Rate Regions for Interference Channels With Degraded Message Sets

The interference channel with degraded message sets (IC-DMS) refers to a communication model, in which two senders attempt to communicate with their respective receivers simultaneously through a common medium, and one sender has complete and a priori (noncausal) knowledge about the message being transmitted by the other. A coding scheme that collectively has advantages of cooperative coding, collaborative coding, and dirty paper coding, is developed for such a channel. With resorting to this coding scheme, achievable rate regions of the IC-DMS in both discrete memoryless and Gaussian cases are derived. The derived achievable rate regions generally include several previously known rate regions as special cases. A numerical example for the Gaussian case further demonstrates that the derived achievable rate region offers considerable improvements over these existing results in the high-interference-gain regime.      

On Fast-Decodable Space–Time Block Codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for $2times2$ and $4times2$ multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable $2times2$ STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity $4times2$ STBC, and show that it outperforms all previously known codes with certain constellations.      

Weil-Serre Type Bounds for Cyclic Codes

We give a new method in order to obtain Weil-Serre type bounds on the minimum distance of arbitrary cyclic codes over ${BBF}_{p^e}$ of length coprime to $p$, where $e ge 1$ is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when $e=1$ or $e=2$ using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil–Serre type bounds in various cases. By examples we show that our bounds perform very well against Bose–Chaudhuri–Hocquenghem (BCH) bound and they yield the exact minimum distance in some cases.      

Nonlinear Influence of T-Channels in an in silico Relay Neuron

Thalamic relay cells express distinctive response modes based on the state of a low-threshold calcium channel (T-channel). When the channel is fully active (burst mode), the cell responds to inputs with a high-frequency burst of spikes; with the channel inactive ( tonic mode), the cell responds at a rate proportional to the input. Due to the T-channel's dynamics, we expect the cell's response to become more nonlinear as the channel becomes more active. To test this hypothesis, we study the response of an in silico relay cell to Poisson spike trains. We first validate our model cell by comparing its responses with in vitro responses. To characterize the model cell's nonlinearity, we calculate Poisson kernels, an approach akin to white noise analysis but using the randomness of Poisson input spikes instead of Gaussian white noise. We find that a relay cell with active T-channels requires at least a third-order system to achieve a characterization as good as a second-order system for a relay cell without T-channels.      

Sensitivity and Spatial Resolution of Transvenous Leads in Implantable Cardioverter Defibrillator

It has been previously documented that the main features and sensing performance of electrograms (EGMs) recorded in implantable cardioverter defibrillators (ICDs) depend on lead configuration. Although this dependence has been ascribed to differences in lead sensitivity and spatial resolution, the quantification of these two properties on ICD has not yet been attempted. In this paper, an operative framework to study the spatial resolution of ICD transvenous leads is presented. We propose to quantify the spatial resolution of ICD transvenous leads based on a new characterization called lead resolution volume (ResV). We analyzed the sensitivity distribution and the ResV of two unipolar (tip–can and coil–can ) and two bipolar (true or tip–ring and integrated or tip–coil) ICD transvenous lead configurations. A detailed 3-D model of the human thorax based on the visible human man dataset was used to compute the lead sensitivity and computer simulations of simple cardiac dynamics were used to quantify the ResV. Differences in the sensitivity distribution throughout the ventricular myocardium (VM) were observed for each lead configuration. In our computer model of the human thorax, the ResV was found to comprise 7%, 35%, 45%, and 70% of the VM for true bipolar, integrated bipolar, tip–can unipolar, and coil–can unipolar ICD leads, respectively. Furthermore, our analysis shows that the spatial resolution depends on both lead sensitivity and cardiac dynamics, and therefore, it can vary for different heart rhythms.