Michael A. Lexa

Distributed Structures, Sequential Optimization, and Quantization for Detection

In the design of distributed quantization systems, one inevitably confronts two types of constraints - those imposed by a distributed systems structure and those imposed by how the distributed system is optimized. Structural constraints are inherent properties of any distributed quantization system and are normally summarized by functional relationships defining the inputs and outputs of their component quantizers. The use of suboptimal optimization methods are often necessitated by the computational complexity encountered in distributed problems. This correspondence briefly explores the impact and interplay of these two types of constraints in the context of distributed quantization for detection. We introduce two structures that exploit interquantizer communications and that represent extremes in terms of their structural constraints. We then develop a sequential optimization scheme that maximizes the Kullback-Leibler divergence, takes advantage of statistical dependencies in the distributed systems output variables, and leads to simple parameterizations of the component quantization rules. We present an illustrative example from which we draw insights into how these constraints influence the quantization boundaries and affect performance relative to lower and upper bounds.

To cooperate or not to cooperate: detection strategies in sensor networks

This paper is an initial investigation into the following question: can cooperation among sensors in a sensor network improve detection performance in a simple hypothesis test? We analyze a simple cooperative system using the Kullback-Leibler (KL) discrimination distance and a quantity known as the information transfer ratio which is a ratio of KL distances. We discover that, asymptotically, gain over a non-cooperative system depends on the conditional KL distance. We conclude with an illustrative example which demonstrates that cooperation not only significantly improves performance but can also degrade it.

A new look at the informational gain of soft decisions

The 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.

An information processing approach to distributed detection

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 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.

Optimizing binary decision systems by manipulating transmission intervals

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 Chemoff 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, D.H. and Rodriguez-Diaz, H., 2003] wherein the gains of unequal bit transmissions are studied in terms of minimum squared error.

Information processing ability of binary detectors and block decoders

This paper applies the concepts of information processing [S. Sinanovic et al., Jun. 2002] to the study of binary detectors and block decoders in a single user digital communication system. We quantify performance in terms of the information transfer ratio /spl gamma/ which measures how well systems preserve discrimination information between two stochastic signals. We investigate hard decision detectors and minimum distance decoders in various additive noise environments. We show that likelihood ratio digital demodulators maximize /spl gamma/.