The sampling window (Corresp.)

The concept of the sampling window is introduced for the central interpolation of finite energy band-limited functions. The sampling window does not increase the rate of convergence of the truncation error series, as do various convergence factors, but does significantly reduce the truncation-error bound.     

Permutation codes for discrete channels (Corresp.)

A class of nonlinear codes for discrete channels is defined with the use of permutation groups. Several examples of such codes are given; their parameters are similar to those for Reed-Solomon codes in some cases. Decoding algorithms are discussed.     

On the performance of a nonparametric detection scheme for dependent data (Corresp.)

A nonparametric scheme for detecting a constant signal embedded in m-dependent noise is cousidered, aud the performance of the detector in both the asymptotic case and the case of a finite number of samples is investigated. It is shown that the design of the detector with a finite amount of data can be radically different from the design based upon the asymptotic limit.     

Linear block codes for error detection (Corresp.)

The probability of undetected error of linear block codes for use on a binary symmetric channel is investigated. Upper hounds are derived. Several classes of linear block codes are proved to have good error-detecting capability.     

Encoding message lengths for data transmission (Corresp.)

Two familiar techniques for encoding message lengths are considered. One technique breaks messages into packets, with each but the last message packet having the same length. The message length is encoded by specifying the last packet and its length. The other technique uses a special bit sequence called a flag to terminate the message and slightly re-encodes the message to prevent the flag from appearing within the message. For a geometric message length distribution and for properly chosen parameters, it is shown that the packet strategy is optimal in the Huffman coding sense and that the flag strategy is very close to optimal. Moreover, for a given expected message length the expected codeword lengths are quite insensitive to the message length distribution.     

Entropy and data compression (Corresp.)

An optimum compression ratio (OCR) is defined for a source, leading to "efficiency" of a compression algorithm and resulting in a good evaluation of data-compression schemes. Applications to first- and second-order Markov sources, in conjunction with the "fan" and "zero-order hold" compression schemes, are also presented.     

Averaging logarithms for detection and estimation (Corresp.)

In a number of applications in signal processing it is desirable to estimate the logarithm of the average of noisy physical measurements by averagingMindependent logarithms of the measurements. Only a modest number of bits are necessary in the logarithmic averaging process, which is used in logarithmic radar receivers to improve the effective dynamic range where post-detection averaging occurs, and in ensemble averaging spectral coefficients prior to the detection decision. A knowledge of the estimation error and of the detectability loss becomes important in these applications. This correspondence extends and generalizes Green's work in detection using averaged logarithms and presents an averaging loss methodology for continuousM. It gives numerical detectability loss results for a representative detection criterion. It contains further results on estimation accuracy attainable from summed logarithms, including numerical results for estimation error as a function ofMand SNR.     

Signal detection under mismatch (Corresp.)

A binary detection problem of the Neymann-Pearson type, in which the probability density functions used are inaccurate versions of the true ones, are considered. The performance of the above suboptimal detection scheme as the number of observations increases is investigated. A necessary and sufficient condition is given for the exponential convergence to zero of the two error probabilities as the number of observations increases. The condition is in terms of an inequality between differences of asymptotic per sample informational divergence expressions.     

On the detection problem (Corresp.)

The detection problem for the model "signal-plus-noise," where the "noise" is represented by a Wiener process, has been approached primarily through the use of martingale theory. There are two core results: a new version of what is called "Girsanov's theorem" and the fact that the Wiener measure on the space of continuous functions can be generated by any Wiener process. In this correspondence a new version of "Girsanov's theorem" is derived and some fragmentary results concerning the measures associated with martingales are presented.     

Partial feedback for the discrete memoryless multiple access channel (Corresp.)

The region Cover and Leung found for the discrete memoryless multiple access channel with feedback to both encoders is proved achievable also with feedback to only one encoder. The novel ideas of nonrandom partitions and restricted decoding are used to avoid list coding techniques.     

On exponential smoothing of discrete time series (Corresp.)

Thekth-order exponential filter is analyzed using a two-dimensionalztransform. The weighting functions for both the data and the initial conditions are derived.     

Using codes for error correction and detection (Corresp.)

A linear codeCover GF(q)is good fort-error-correction and error detection ifP(C,t;epsilon) leq P(C,t;(q - 1)/q)for allepsilon, 0 leq epsilon leq (q - 1)/q, whereP(C, t; epsilon)is the probability of an undetected error after a codeword inCis transmitted over aq-ary symmetric channel with error probabilityepsilonand correction is performed for all error patterns withtor fewer errors. A sufficient condition for a code to be good is derived. This sufficient condition is easy to check, and examples to illustrate the method are given.     

Sequential detection between Poisson processes (Corresp.)

The problem of sequential detection between Poisson processes is analyzed and resolved. Wald's results on sequential analysis are used, but a substantial modification is shown to be necessary due to the discontinuous nature of the likelihood ratio. It is shown that, in general, one can take into account the "excess over the boundary" so as to design sequential tests with a given error performance.     

Optimal detection of FM clicks (Corresp.)

For the Case of an unmodulated carrier, the detection of an FM click is formulated as the detection of a non-Gaussian random signal embedded in colored Gaussian noise. This correspondence presents an approximation to the optimum detector of FM clicks along with its theoretical performance in terms of probability of false alarm and probability of error. Numerical results are presented in graphical form. The corresponding exact results for detection problems of this type are currently not available. The theoretical results help to explain the known practical result that FM threshold extenders are limited to threshold improvements of only a few dB. For the case of a modulated carrier, some comments concerning detector performance are presented. For comparison purposes, detector performance of a detector based on the heights of local maxima is also presented.     

Nonparametric detection using dependent samples (Corresp.)

A new general approach to the formulation of a non-parametric detector using dependent samples is introduced and applied to a space-diversity system employing dc signaling. A comparison based on a form of asymptotic relative efficiency is made between the new detector and a Mann-Whitney detector. Under certain conditions the new procedure demonstrates an improvement in transmission efficiency.     

Robust detection to stochastic signals (Corresp.)

In this correspondence we evaluate both the large and small sample performance of a limiter-quadratic detector (LQD) for the detection of a Gaussian signal in non-Gaussian noise. The LQD is shown to be robust for small as well as large sample sizes.     

Photon counting and Laguerre detection (Corresp.)

In this correspondence maximum-likelihood binary detection theory is applied to an incoherent optical system model employing photodetectors governed by Laguerre counting statistics. It is shown that a maximum-likelihood Laguerre detector corresponds to a count comparison over each signaling interval. Laguerre error probabilities are presented and compared with those for Poisson counting.