Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

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Bit-Interleaved Coded Modulation

Matrix Differential Calculus with Applications in Statistics and Econometrics

Generalized Linear Models (2nd ed.)

The large deviation approach to statistical mechanics

Clinical Trials: A Practical Approach

We show that the Adaptive Coherence Estimator (ACE) is a uniformly most powerful (UMP) invariant detection statistic. This statistic is relevant to a scenario appearing in adaptive array processing, in which there are auxiliary, signal-free, training-data vectors that can be used to form a sample covariance estimate for clutter and interference suppression. The result is based on earlier work by Bose and Steinhardt, who found a two-dimensional (2-D) maximal invariant when test and training data share the same noise covariance. Their 2-D maximal invariant is given by Kelly's Generalized Likelihood Ratio Test (GLRT) statistic and the Adaptive Matched Filter (AMF). We extend the maximal-invariant framework to the problem for which the ACE is a GLRT: The test data shares the same covariance structure as the training data, but the relative power level is not constrained. In this case, the maximal invariant statistic collapses to a one-dimensional (1-D) scalar, which is also the ACE statistic. Furthermore, we show that the probability density function for the ACE possesses the property of "total positivity," which establishes that it has monotone likelihood ratio. Thus, a threshold test on the ACE is UMP-invariant. This means that it has a claim to optimality, having the largest detection probability out of the class of detectors that are also invariant to affine transformations on the data matrix that leave the hypotheses unchanged. This requires an additional invariance not imposed by Bose and Steinhardt: invariance to relative scaling of test and training data. The ACE is invariant and has a Constant False Alarm Rate (CFAR) with respect to such scaling, whereas Kelly's GLRT and the AMF are invariant, and CFAR, only with respect to common scaling.

The adaptive coherence estimator: a uniformly most-powerful-invariant adaptive detection statistic

Preface 1. Fundamental approximations 2. Properties and derivatives 3. Multivariate densities 4. Conditional densities and distribution functions 5. Exponential families and tilted distributions 6. Further exponential family examples and theory 7. Probability computation with p* 8. Probabilities with r*-type approximations 9. Nuisance parameters 10. Sequential saddlepoint applications 11. Applications to multivariate testing 12. Ratios and roots of estimating equations 13. First passage and time to event distributions 14. Bootstrapping in the transform domain 15. Bayesian applications 16. Non-normal bases References Index.

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Saddlepoint approximations with applications.

We show that the familiar bootstrap plug-in rule of Efron has a natural analog in finite population settings. In our method a characteristic of the population is estimated by the average value of the characteristic over a class of empirical populations constructed from the sample. Our method extends that of Gross to situations in which the stratum sizes are not integer multiples of their respective sample sizes. Moreover, we show that our method can be used to generate second-order correct confidence intervals for smooth functions of population means, a property that has not been established for other resampling methods suggested in the literature. A second resampling method is proposed that also leads to second-order correct confidence intervals and is less computationally intensive than our bootstrap. But a simulation study reveals that the second method can be quite unstable in some situations, whereas our bootstrap performs very well.

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Bootstrap Methods for Finite Populations

In standard saddlepoint approximations to the cumulative distribution function of a random variable, the normal distribution has appeared to play a special role. In this article we consider what happens when the normal “base” distribution is replaced by an arbitrary base distribution. Generalized versions of several standard formulas, are presented. The choice of a chi-squared base or an inverse Gaussian base is then considered in detail. The generalized approximations are compared in two examples: a linear combination of chi-squared variables and the first passage time distribution for a random walk. The former example considers approximations using the chi-squared base that are slightly more accurate than their normal-based counterparts. In the latter example, approximations based on the inverse Gaussian are considerably more accurate than their normal-based counterparts.

Ronald W. Butler

Papers

The adaptive coherence estimator: a uniformly most-powerful-invariant adaptive detection statistic

Saddlepoint approximations with applications.

Bootstrap Methods for Finite Populations

Saddlepoint Approximations to the CDF of Some Statistics with Nonnormal Limit Distributions

Laplace approximation for Bessel functions of matrix argument