Jake Gunther

Entropy Minimization for Solving Sudoku

Solving Sudoku puzzles is formulated as an optimization problem over a set of probabilities. The constraints for a given puzzle translate into a convex polyhedral feasible set for the probabilities. The solution to the puzzle lies at an extremal point of the polyhedron where the probabilities are either zero or one and the entropy is zero. Because the entropy is positive at all other feasible points, an entropy minimization approach is adopted to solve Sudoku. To escape local entropy minima at nonsolution extremal points, a search procedure is proposed in which each iteration involves solving a simple convex optimization problem. This approach is evaluated on thousands of puzzles spanning four levels of difficulty from “easy” to “evil”.

Learning Echo Paths During Continuous Double-Talk Using Semi-Blind Source Separation

Echo cancelers typically employ control mechanisms to prevent adaptive filter updates during double-talk events. By contrast, this paper exploits the information contained in time-varying second order statistics of nonstationary signals to update adaptive filters and learn echo path responses during double-talk. First, a framework is presented for describing mixing and blind separation of independent groups of signals. Then several echo cancellation problems are cast in this framework, including the problem of simultaneous acoustic and line echo cancellation as encountered in speaker phones. A maximum-likelihood approach is taken to estimate both the unknown signal statistics as well as echo canceling filters. When applied to speech signals, the techniques developed in this paper typically achieved between 30 and 40 dB of echo return loss enhancement (ERLE) during continuous double-talking.

Detection of Amorphously Shaped Objects Using Spatial Information Detection Enhancement (SIDE)

Pattern recognition of amorphously shaped objects such as gas plumes, oil spills, or epidemiological spread is difficult because there is no definite shape to match. We consider detection of such amorphously shaped objects using a neighborhood model which operates on a concept of loose spatial contiguity: there is a significant probability that a pixel surrounded by the object of interest itself contains that object of interest, and boundaries tend to be smooth. These assumptions are distilled into a single-parameter prior probability model to use in a maximum a posteriori hypothesis test. The method is evaluated against synthetic data generated from hyperspectral imagery and DIRSIG simulation results. These tests indicate significant improvement on the ROC curves.

On the Spectral Efficiency of Rate and Subcarrier Bandwidth Adaptive OFDM Systems Over Very Fast Fading Channels

In this paper, rate and subcarrier bandwidth adaptation (RSBA) on the average spectral efficiency of orthogonal frequency-division multiplexing (OFDM) systems using M-ary quadrature amplitude modulation (M-QAM) is investigated in the presence of frequency-selective and very rapidly time-varying fading channels. The closed-form expressions for rate and capacity with perfect channel state information (CSI) and imperfect CSI are derived. In this paper, imperfect CSI is caused jointly by channel estimation error and unavoidable delay between when CSI is estimated and when the estimation results are used for actual transmission. The capacity with perfect CSI is just a special case of imperfect CSI. Based on the closed-form expressions of the maximum capacity, optimal RSBA algorithms with perfect and imperfect CSI are proposed, respectively. Theoretical and numerical results show that the RSBA scheme can improve the system performance effectively under the perfect-CSI case. It can make a tradeoff between intercarrier interference (ICI) and transmission efficiency by considering the cyclic prefix. The results also show that the RSBA scheme is effective in repelling the impact of outdated CSI, as well as in reducing the impact of channel estimation error, but to a lesser extent.

Burst mode synchronization of QPSK on AWGN channels using kurtosis

This paper explores the use of kurtosis in synchronizing with a QPSK burst transmission. The start and end of the burst are a priori unknown and are detected without the use of pilot signals. After frame level synchronization, signal level synchronization is performed. The symbol timing, carrier frequency and carrier phase are recovered without the assistance of known symbols or synchronization words in the data stream, i.e. totally blind synchronization. The performance of frame, symbol and carrier synchronization algorithms is evaluated through computer simulations.

Maximum likelihood synthetic aperture radar image formation for highly nonlinear flight tracks

This paper develops a flexible time-domain SAR imaging algorithm that is capable of accounting for somewhat arbitrary flight track geometries and platform orientations. The proposed technique casts SAR imaging as a maximum likelihood estimation problem where the ground reflectivities are taken as the parameters to be estimated. It is shown that conventional back projection is one of two steps required to form the optimal maximum likelihood image. Simulation examples are given that compare images and impulse response functions for back projection and the maximum likelihood algorithm.

Minimum Bayes Risk Adaptive Linear Equalizers

This paper introduces Bayes risk (expected loss) as a criterion for linear equalization. Since the probability of error is equal to the Bayes risk (BR) for a particular binary loss function, this work is a natural generalization of previous works on minimum probability of error (PE) equalizers. Adaptive equalization algorithms are developed that minimize the BR. Like the minimum PE equalizers, the BR algorithms have low computational complexity which is comparable to that of the LMS algorithm. The advantage of the BR criterion is that the loss function can be specified in a manner that accelerates adaptive equalizer convergence relative to the minimum PE adaptive algorithm as illustrated in simulation examples. Besides introducing a new criterion, this paper provides another independent contribution to the field of PE minimizing equalization. While most prior works focus on M-ary QAM type modulations with rectangular decision regions, this paper uses upper bounds on the probabilities of certain events to yield tractable mathematics that apply to two-dimensional constellations with arbitrarily shaped decision regions. The resulting adaptive algorithm use the full information available in the phase of the error signal, whereas previous algorithms use a quantized version of this error phase.

Description of EduCOM: A graphical modeling and programming language for teaching and learning digital communication systems

This paper presents EduCOM, a graphical language for teaching and learning digital communication systems. In EduCOM students build graphical models (i.e., block diagrams) of digital communication transmitters, channels, and receivers. Then EduCOM creates the shell of a C/C++ code realization of the graphical model, but it leaves the implementation of each block empty so that students are required to implement the functionality of the blocks in a low‐level programming language such as C/C++. Therefore, EduCOM goes beyond passive drag–drop‐connect style activities and forces students to think more deeply about each operation performed on the signals in the system, and preliminary assessment results with a small set of students bear this point out. Students indicated that the mixture of graphical modeling and low‐level programming provided by EduCOM is an improvement over pure graphical modeling or pure low‐level programming in helping them learn about communication systems.

A Generalized BCJR Algorithm and Its Use in Iterative Blind Channel Identification

The well-known Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm was generalized to compute joint posterior probabilities of arbitrary sets of symbols given noisy observations of those symbols at the output of an intersymbol interference (ISI) channel. This letter explores using pair-wise joint posterior probabilities produced by generalized BCJR together with expectation maximization for blind identification of the ISI channel impulse response and noise variance. Simulations indicate that the blind algorithm accurately estimates the channel response and noise variance and yields bit error rates comparable to a channel-informed BCJR equalizer.

Minimum Symbol Error Rate Carrier Phase Recovery of QPSK

This paper considers the problem of phase recovery of QPSK signals with phase-locked loops (PLL) using two new phase error detectors (PEDs) which are designed to minimize the probability of making a symbol decision error. The new PEDs resemble the PED derived from the maximum likelihood criterion. However, the new PEDs penalize matched filter outputs that are close to decision region boundaries. This penalty gives rise to faster converging PLLs relative to PLLs using the maximum likelihood PED, as shown in simulation results. The S-curves for the PEDs are used as a tool to gain insight into the behavior of the new PEDs.