Browsing by Author "Lexa, Michael"
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Item Broadcast Detection Structures with Applications to Sensor Networks(2007) Johnson, Don; Lexa, Michael; Digital Signal Processing (http://dsp.rice.edu/)Data broadcasting is potentially an effective and efficient way to share information in wireless sensor networks. Broadcasts offer energy savings over multiple, directed transmissions, and they provide a vehicle to exploit the statistical dependencies often present in distributed data. In this paper, we examine two broadcast structures in the context of a distributed detection problem whose inputs are statistically dependent. Specifically, we develop a suboptimal approach to maximize the Kullback-Leibler divergence over a set of binary quantization rules. Our approach not only leads to simple parameterizations of the quantization rules in terms of likelihood ratio thresholds, but also provides insight into the inherent constraints distributed structures impose. We then present two examples in detail and compare the performance of the broadcast structures to that of a centralized system and a noncooperative system. These examples suggest that in situations where the detection problem is difficult (small input divergence), broadcasting solitary bits (or even nothing at all) may be nearly as effective as broadcasting real-valued observations.Item An Information processing approach to distributed detection(2003-09-20) Lexa, Michael; Johnson, Don; Digital Signal Processing (http://dsp.rice.edu/)We apply the recent theory of information processing to a hybrid distributed detection architecture that combines the traditional parallel and tandem architectures. Central to this theory is the Kullback-Leibler discrimination distance and quantity known as the information transfer ratio, defined as defined as the ratio of the KL distances between the distributions characterizing the input and output of a system. We characterize the asymptotic performance of proposed hybrid system and compare it with the performance of the parallel, tandem and centralized architectures. We conclude with an illustrative example.Item Information processing of linear block decoders(2002-10-20) Lexa, Michael; Johnson, Don; Digital Signal Processing (http://dsp.rice.edu/)This paper develops a systematic method of studying the benefits of soft decoding for linear block codes by applying the concepts of information processing. We show that soft decoding uniformly improves decoder performance in terms of the information transfer ratio.Item A new look at the informational gain of soft decisions(2003-04-20) Lexa, Michael; Johnson, Don; Digital Signal Processing (http://dsp.rice.edu/)This paper develops a new systematic method of studying the benefits of 2-bit soft decisions by applying the concepts of information processing theory. We quantify performance in terms of the information transfer ratio and demonstrate the performance gain over hard decision detectors in several noise environments. In addition, we show that likelihood ratio tests maximize the information transfer ratio, and we propose a method of optimizing threshold values for the 2-bit soft decision detector.Item Optimizing binary decision systems by manipulating transmission intervals(2003-07-20) Lexa, Michael; Johnson, Don; Digital Signal Processing (http://dsp.rice.edu/)We study the optimization of a binary decision system where quantized (soft) decisions are transmitted across an additive white Gaussian noise channel. We adjust the bit transmission intervals to maximize the Chernoff distance at the output of the channel. At low channel signal-to-noise ratios (when the probability of a bit error is higher), we find unequal transmission intervals yield significant gains in terms of Chernoff distance and the information transfer ratio over the equal transmission case. This paper is a companion paper to Johnson and Rodriguez-Diaz (2003) wherein the gains of unequal bit transmissions are studied in terms of minimum squared error.Item Remembering John Napier and His Logarithms(2002-05-20) Lexa, MichaelThis article describes John Napier's original defintion of logarithms and presents his method of tabulation for the first logarithmic table. Napier's logarithms are found to have an intimate relationship with the natural exponential function but predates the work of Euler by about a hundred years.Item Useful Facts about the Kullback-Leibler Discrimination Distance(2004-12-01) Lexa, MichaelThis report contains a list of some of the more prominent properties and theorems concerning the Kullback-Leibler (KL) discrimination distance. A brief discussion is also provided indicating the type of problems in which the KL distance has been applied. References are provided for the reader's convenience.