New bounds for the Marcum Q-function

New bounds are proposed for the Marcum Q-function, which is defined by an integral expression where the 0th-order modified Bessel function appears. The proposed bounds are derived by suitable approximations of the 0th-order modified Bessel function in the integration region of the Marcum Q-function. They prove to be very tight and outperform bounds previously proposed in the literature. In particular, the proposed bounds are noticeably good for large values of the parameters of the Marcum Q-function, where previously introduced bounds fail and where exact computation of the function becomes critical due to numerical problems     

Integral representation and bounds for Marcum Q-function

A new expression for the Marcum Q-function involving an integral over a fixed interval is given. Tight upper and lower bounds are then derived and applied to the performance evaluation of noncoherent and differentially coherent detection of digital modulation over Nakagami fading channels     

Information-theoretic upper and lower bounds for statistical estimation

In this paper, we establish upper and lower bounds for some statistical estimation problems through concise information-theoretic arguments. Our upper bound analysis is based on a simple yet general inequality which we call the information exponential inequality. We show that this inequality naturally leads to a general randomized estimation method, for which performance upper bounds can be obtained. The lower bounds, applicable for all statistical estimators, are obtained by original applications of some well known information-theoretic inequalities, and approximately match the obtained upper bounds for various important problems. Moreover, our framework can be regarded as a natural generalization of the standard minimax framework, in that we allow the performance of the estimator to vary for different possible underlying distributions according to a predefined prior     

VVMOS power transistors: upper and lower bounds of the on-resistance

The estimation of the n? drift layer resistance Rn? of power VVMOS (V-groove vertical-geometry power MOST) devices is treated in the letter. The obtained results, based on the possibility of defining upper and lower bounds of the accurate value, are compared with experimental and theoretical results of other methods.     

Universal linear least squares prediction: upper and lower bounds

We consider the problem of sequential linear prediction of real-valued sequences under the square-error loss function. For this problem, a prediction algorithm has been demonstrated whose accumulated squared prediction error, for every bounded sequence, is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a given order p. The redundancy, or excess prediction error above that of the best predictor for that sequence, is upper-bounded by A/sup 2/P ln(n)/n, where n is the data length and the sequence is assumed to be bounded by some A. We provide an alternative proof of this result by connecting it with universal probability assignment. We then show that this predictor is optimal in a min-max sense, by deriving a corresponding lower bound, such that no sequential predictor can ever do better than a redundancy of A/sup 2/p ln(n)/n.     

Estimation of lower and upper bounds on the power consumption fromscheduled data flow graphs

In this paper, we present an approach for the calculation of lower and upper bounds on the power consumption of data path resources like functional units, registers, I/O ports, and busses from scheduled data flow graphs executing a specified input data stream. The low power allocation and binding problem is formulated. First, it is shown that this problem without constraining the number of resources can be relaxed to the bipartite weighted matching problem which is solvable in O(n)³. n is the number of arithmetic operations, variables, I/O-access or bus-access operations which have to be bound to data path resources. In a second step we demonstrate that the relaxation can be efficiently extended by including Lagrange multipliers in the problem formulation to handle a resource constraint. The estimated bounds take into account the effects of resource sharing. The technique can be used, for example, to prune the design space in high-level synthesis for low power before the allocation and binding of the resources. The application of the technique on benchmarks with real application input data shows the tightness of the bounds     

Exponential-type bounds on the generalized Marcum Q-function withapplication to error probability analysis over fading channels

Strict upper and lower bounds of exponential-type are derived for the generalized (mth order) Marcum Q-function which enable simple evaluation of a tight upper bound on the average bit-error probability performance of a wide class of noncoherent and differentially coherent communication systems operating over generalized fading channels. For the case of frequency selective fading with arbitrary statistics per independent fading path, the resulting upper hound on performance is expressed in the form of a product of moment generating functions of the instantaneous power random variables that characterize these paths     

A sequence of upper and lower bounds for the Q function (Corresp.)

A sequence of upper and lower bounds for theQfunction defined asQ(x)= 1/ sqrt{2 pi} int_{x}^{infty} exp[(-y^{2})/2]dyis developed. These bounds are shown to be tighter than those most commonly used.     

Moment space upper and lower error bounds for digital systems with intersymbol interference

A method for the evaluation of upper and lower bounds to the error probability of a linear pulse-amplitude modulation (PAM) system with bounded intersymbol interference and additive Gaussian noise is obtained via an isomorphism theorem from the theory of moment spaces. These upper and lower bounds are seen to be equivalent to upper and lower envelopes of some compact convex body generated from a set of kernel functions. Depending on the selection of these kernels and their corresponding moments, different classes of bounds are obtained. In this paper, upper and lower bounds that depend on the absolute moment of the intersymbol interference random variable, the second moment, the fourth moment, and an "exponential moment" are found by analytical, graphical, or iterative approaches. We study in detail the exponential moment case and obtain a family of new upper and a family of new lower bounds. Within each family, expressions for these bounds are given explicitly as a function of an arbitrary real-valued parameter. For two channels of interest, upper and lower bounds are evaluated and compared. Results indicate these bounds to be tight and useful.     

Beam pattern synthesis for line arrays subject to upper and lower constraining bounds

A technique is described for synthesizing the coefficients of an antenna array which satisfy a constrained minimax criterion. Inhibition regions can be formed in the beam pattern and placed advantageously in directions associated with strong sources of interference. Modified Dolph-Chebyshev beam patterns are obtained by imposing upper and lower constraining bounds on the beam pattern over regions of directions in space. Specific examples are presented for line arrays.     

New upper bounds on error exponents

We derive new upper bounds on the error exponents for the maximum-likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the best earlier known bounds by Shannon-Gallager-Berlekamp (1967) and McEliece-Omura (1977). For the probability of undetected error the new bounds are better than the bounds by Levenshtein (1978, 1989) and the bound by Abdel-Ghaffar (see ibid., vol.43, p.1489-502, 1997). Moreover, we further extend the range of rates where the undetected error exponent is known to be exact. The new bounds are based on an analysis of possible distance distributions of the codes along with some inequalities relating the distance distributions to the error probabilities     

New upper bounds on generalized weights

We derive new asymptotic upper bounds on the generalized weights of a binary linear code of a given size. We also prove some asymptotic results on the distance distribution of binary codes     

Improved upper bounds on sizes of codes

Let A(n,d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n,d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n,d) for n⩽28 are improved     

Tight upper bounds on the redundancy of Huffman codes

Bounds on the redundancy of Huffman codes in terms of the probability p₁ of the most likely source letter are provided. In particular, upper bounds are presented that are sharper than the bounds given recently by R.G. Gallager (ibid., vol.IT-24, no.6, p.668-74, Nov.1978) and by R.M. Capocelli et al. (ibid., vol. IT-32, no.6, p.854-857, Nov. 1986) for an interval 2/(2^l+1+1)<p₁<1/(2^l-1), l⩾2. It is shown that the new bounds are the tightest possible for these intervals     

New upper and lower bounds line of sight path loss model for mobile propagation in buildings

This paper proposes a method to predict line-of-sight (LOS) path loss in buildings. We performed measurements in two different types of buildings at a frequency of 1.8 GHz and propose a new path loss model with its upper and lower bounds. The upper and lower bounds depend on max and min values of sampled path loss data. This makes our model limit path loss within the boundary lines. The model includes time-variant effects from the object movement from people in the building and cars in parking areas. These influence reasonably on wave propagation. The results have shown that the proposed model will be useful for the design of the indoor wireless communication systems.     

Some lower bounds on signal parameter estimation

New bounds are presented for the maximum accuracy with which parameters of signals imbedded in white noise can be estimated. The bounds are derived by comparing the estimation problem with related optimal detection problems. They are, with few exceptions, independent of the bias and include explicitly the dependence on the a priori interval. The new results are compared with previously known results.     

Sphere-packing upper bounds on the free distance of trellis codes

Sphere-packing arguments are used to develop upper bounds on the free distance of trellis codes. A general bounding procedure is presented. Sphere packing bounds, including bounds on the density of infinite regions, packings for hypercubes, and packings on the surface of a unit sphere, are then used to produce bounds for a wide variety of trellis codes. Among the applications are convolutional codes, Ungerboeck codes for phase-shift keying and quadrature amplitude modulation, coset codes, and continuous phase modulation codes. The new bounds are significantly tighter than existing bounds in many cases of practical interest     

A note on lower bounds (Corresp.)

A new lower bound for the parameters of (nonlinear)q-ary codes is introduced. For some q this bound improves on the Varshamov-Gilbert bound, the "modular" algebraic-geometric bound, and the very recent Vlbreve{a}duts bound.     

Computing lower bounds on functional units before scheduling

The authors present a new polynomial-time algorithm for computing lower bounds on the number of functional units (FUs) of each type required to schedule a data flow graph in a specified number of control steps. A formal approach is presented that is guaranteed to find the tightest possible bounds that can be found by relaxing either the precedence constraints or integrality constraints on the scheduling problem. This tight, yet fairly efficient, bounding method can be used to estimate FU area, to generate resource constraints for reducing the search space, or in conjunction with exact techniques for efficient optimal design space exploration