Showing papers on "Word error rate published in 1973"

An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis1

Abstract: Summary When a sample discriminant function is computed, it is desired to estimate the error rate using this function. This is often done by computing G(-D/2), where G is the cumulative normal distribution and D2 is the estimated Mahalanobis' distance. In this paper an asymptotic expansion of the expectation of G(-D/2) is derived and is compared with existing Monte Carlo estimates. The asymptotic bias of G(-D/2) is derived also and the well-known practical result that G(-D/2) gives too favourable an estimate of the true error rate

Binary Error Rate Caused by Intersymbol Interference and Gaussian Noise

Abstract: The probability of error in a binary signal owing to intersymbol interference and Gaussian noise is computed by approximation of the expression for the probability of error by a finite sum of squareintegrable functions. The approximating functions should be chosen so that their averages over all bit combinations can be easily determined. The projection of the error function on the subspace of polynomials results in a series which converges more rapidly to the exact error rate than does the Taylor series expansion used previously. The negative exponential functions have the same general form as the error function and, as expected, also result in rapid convergence to the average error rate.

The Word Problem for Absolute Presentations

Abstract: Presentations (both relative and absolute) of a group G are methods of describing G. Essentially, we pick a set of generators for G and then find some way of enumerating the multiplication table of G. We do this by forming all" words " in the generators, and then show how to pick the words which represent the identity of G (in the relative case), and also the words which do not represent the identity of G (in the absolute case). The following facts are common to both relative and absolute presentations. An alphabet A is any finite or countable set. It is convenient to assume that 1 $A. The members of A are called letters. We form from A the words over A by use of concatenation, use of " 1 " , and the symbol " 1". Thus

A review of multiple amplitude-phase digital signals

Abstract: This paper reviews the data rate, error rate, and signal-to-noise ratio relationship for various uncoded M-ary digital amplitude modulation (AM), phase modulation (PM), and combined AM-PM systems. These signal systems have the common virtue that expanding the number of possible signals to be transmitted increases the data rate but not the bandwidth. A general treatment of the error rate of M-ary digital AM-PM permits development of a simple yet accurate expression which approximates the increase in average signal-to-noise ratio (over that of binary phase shift keying) required for constant error performance. This equation provides insight into why arrays differ in their signal-to-noise ratio requirements.

Performance of Jointly Optimized Prefilter-Equalizer Receivers

Abstract: A linear receiver for digital communication over unknown dispersive and noisy channels obtained by jointly optimizing the prefilter and equalizer has been described by the authors in a recent paper [4]. An extension to incorporating a decision-feedback equalizer is made. Performance of the new receiver is evaluated by means of computer simulation. Comparison of the performance of the new receiver, the matched filter-equalizer receiver, and the fixed low-pass filter-equalizer receiver is made both with respect to convergence rate and error rate. It is conjectured that the new receiver exhibits performance superior to both the matched filter-equalizer receiver and the fixed low-pass filter-equalizer receiver.

Error Rates on a Data Link with Nonlinear Regeneration

Abstract: A model of nonlinear data wave regeneration without retiming is analyzed. Attention is focused on performance after regeneration and subsequent detection. The communication model consists of a pseudoternary signal that is regenerated at one data station, but not retimed prior to retransmission to another station. The signal regeneration is accomplished by a three-level slicer, and this nonlinear transformation degrades the overall system performance in the presence of noise. The extent of this degradation is our subject matter. The formulation and analysis are constructed so that one can put to effective use the fact that, for a certain Gaussian process, one can give definite expressions for the chance that its sample paths lie below a piecewise linear curve on an appropriately restricted time interval. We are able to use events of this type to give upper and lower bounds for the error rate. The bounds are compared with the error rate that would have been obtained had detection been accomplished before the nonlinear regeneration. We hope that the techniques employed here may be of use in other nonlinear communication problems.

Word Error Rates in Cryptographic Ensembles

Abstract: The word error rate of an ensemble of cryptographic systems is determined. The word error rate is specified as a function of the corresponding plain-text bit error rate. Degradation is defined and computed for the case of phase-shift keying and white Gaussian noise. Finally, the effect of differential encoding on a cryptographic system is investigated.

Statistical properties of gilbert's burst noise model

Abstract: Simple statistical procedures for analyzing error data, e.g., in digital data transmission systems, are usually based on the assumption of independence. This paper studies the performance and potential utility of such simple statistical procedures in the case of nonindependent error occurrences. The burst noise model is selected for this purpose because of its neatness, its mathematical tractability, its built-in structure of dependence, and its importance in communication theory. We show that statistical procedures designed under the assumption of independence tend to be conservative for the burst noise model. For example, the usual binomial test will reject, on the average, more channels with small error rates than it would if the errors were independent. The case that the sample size n and the error rate ρ converge in such a way that nρ→ µ 0 is also studied. It is shown that the error process can be approximated by a compound Poisson process in continuous time t. The statistical implications of this fact are also discussed.

Note on familywise error rates

Abstract: Summary.-An alternative procedure to the use of farnilywise error rates is described that rerains an experimentwise error rate for the entire experiment. The procedure uses Dunm's (1961) test, considering each source of variation as a planned contrast and testing for significance with Dunn's cables. Most of the literature regarding error rates in experimental design has been directed to the one-way analysis of variance situation. Three different kinds of error rates have been faisly widely discussed: per comparison, experimentwise, and per experiment error rates. Ryan (1962 ) has argued effectively for the two latter error rates when interpreting an experiment. A fourth kind of error rate which has received somewhat less attention is the familyzuise error rate. Because the farnilywise error rate has rarely been discussed in textbooks (one notable exception is Miller, 1966), despite the fact that the concept was described much earlier by Tukeyl it would be worthwhile to describe the concept briefly. In the two-way (or higher) analysis of variance, an investigaror might formulate a prio~i hypotheses separately for each source of variacion (rows, columns and interaction), and each source of variacion is viewed as being a separate experiment. In a two-way analysis, when comparisons are made within levels of the A factor at the a level and then comparisons are made separately within the B factor at the a level, the error rate is being controlled at the a level familywise, but at the 2a level experimentwise. It then becomes impocanc for an experimenter to understand the differences between a farnilywise error rate and an experimentwise error rate for the entire experiment. The difference is in one sense mainly conceptual; if the experimenter is willing to interpret each source of variacion as being a separate experiment, chen the farnilywise error rate would be appropriate. While the term farnilywise has usually been given to the multiple comparisons following the main effecc tests, it is useful to extend the term to the main effects and interaction tests rhemselves. When analyzing data in a two-way layout, typically the F test for each main effect and for the interaction are tested independently, using the tabled F values to determine the significance of each separate source of variation in the experiment. The effecc of this practice is to consider each F test as a separate experiment. If each test is performed at the a level, the experimentwise error rate is not held at the u level, but rather at the 1 - ( 1 - a) level. The a level can, 'J. W. Tukey, The problem of multiple comparisons. (Unpublished Notes, Princeton Univer., 1953)