A likelihood ratio formula for spherically invariant processes (Corresp.)

This correspondence provides a likelihood ratio formula for equivalent spherically invariant measures on a real and separable Hilbert space.     

Some geometric properties of the likelihood ratio (Corresp.)

A fundamental spatial property is noted that relates the likelihood ratio for random signals in Gaussian noise to conditional-mean parameter estimation. This allows a geometric interpretation of the estimation-correlation operation. Some additional properties exhibited by the likelihood ratio are also presented.     

A note on the calculation of performance for likelihood ratio processors via computer simulation (Corresp.)

The performance of a likelihood ratio processor must often be determined via computer simulation. This correspondence suggests an effective method of calculating the receiver operating characteristic (ROC) that avoids emphasizing the upper tail region of the likelihood ratio's estimated probability density function. A specific example is presented.     

A Bayes sequential test of m hypotheses (Corresp.)

The problem of sequentially deciding upon one ofmmutually exclusive and exhaustive hypotheses has been studied in detail for the case ofm = 2. This correspondence presents the structure for the Bayesm-ary sequential detector. Computational results depend on a property called subspace separability, which allows one to reduce the dimensionality of the essential averaging process. Numerical results are presented for the case of Gaussian observation statistics andm = 3.     

A class of composite codes (Corresp.)

Certain useful properties of the cyclic codeVare discussed with wordsV(x)=V_{1}(x)(l+x^{n})/(l+x^{n_{1}})+V_{2}(x)(l+x^{n})/(l+x^{n_{2}}), where fori=1,2,V_{i}(x)belongs to a binary codeV_{i}of lengthn_{i}.     

A likelihood ratio formula for two-dimensional random fields

This paper is concerned with the detection of a random signal in white Gaussian noise when both the signal and the noise are two-dimensional random fields. The principal result is the derivation of a recursive formula for the likelihood ratio relating it to certain conditional moments of the signal. It is also shown that, except for some relatively uninteresting cases, a simple exponential formula for the likelihood ratio, such as one has in one dimension, is not possible.     

A method for decoding of generalized Goppa codes (Corresp.)

It is shown how the theory of continued fractions for polynomials can be used for the decoding of a class of codes which contains Goppa codes.     

Mode identification with finite statistics (Corresp.)

The multiple decision problem of identifying the mode of a discrete (k-valued) random variable is examined under a time-varying finite memory constraint. Under the assumption that the distribution of the observed random variable has a unique mode, the partial information model, in which it is assumed that the two largest probabilities can be separated by a known number, is shown to be2kstate perfectly achievable. The general model, in which no assumptions are made on the distribution save the fact that the mode is unique, is shown to be4k (k - 1)state perfectly achievable.     

Unsupervised learning for signal versus noise (Corresp.)

The Bayes solution to the unsupervised sequential learning problem induced by a mixture model for the two-class signal versus noise decision problem generates a computational and storage explosion. A quasi-Bayes approximate learning procedure is proposed that avoids the computational explosion while retaining the flavor of the Bayes solution. Convergence is established and efficiency is investigated.     

Duality for the group-coset probability ratio (Corresp.)

From the MacWilliams and Assmus-Mattson identifies, it is shown that Sullivan's lower bound on the ratio of the probability of a group and a coset has a dual relation with the upper bound.     

A bound for cyclic codes of composite length (Corresp.)

An upper bound on the minimum distance of cyclic codes of composite length is presented. This upper bound proves the BCH bound to be exact for many cyclic codes.     

A bound for arithmetic codes of composite length (Corresp.)

This correspondence presents an upper bound on the minimum distance of arithmetic codes of composite lengthn = n_1 n_2. The tightness of this bound gives a rather good working estimate of the minimum distance of a prospective code.     

A generalized evaluation criterion in parameter estimation (Corresp.)

The choice of the proper evaluation measure is critical for the design of a good parameter estimator. The mean-square     

Two-stage adaptive noise cancellation for intermittent-signal applications (Corresp.)

A novel two-stage adaptive signal extractor for intermittent signal applications is presented. If the presence and absence of the signal can be detected, the first stage will adapt only while the signal is absent and thereby effect a reduction in noise, whereas the second stage will adapt only when the signal is present and thereby effect a reduction in the distortion caused by the gust stage. Bounds on performance are derived, and performance improvement relative to a conventional one-stage adaptive noise canceller is assessed.     

Switching-time statistics for a ramp-excited tunnel diode switch (Corresp.)

An analytical model is developed which yields switching-time jitter statistics for a tunnel diode excited by a current ramp. For appropriate wide-band noise, a "switch sensitivity period" is defined over which a weighted average (a stochastic integral)of the noise specifies the deviation in the switching time. The predictions agree with experimental results.     

Performance bounds for discrimination problems with uncertain statistics (Corresp.)

Decision designs that are insensitive to modeling uncertainty are developed for the Chernoff bounds on the performance of binary hypothesis testing problems. These designs are based on observations with statistical uncertainty modeled by using general classes generated by 2-alternating capacities. The results are illustrated for the two cases of independent identically distributed observations with uncertainty in the probability distribution and discrete-time stationary Gaussian observations with spectral uncertainty, and they are applicable to several other cases as well. For the Chernoff upper bounds on the error probabilities, a "robust" decision design based on the I/kel/hood-ratio test between a least-favorable pair of probability distributions or spectral measures, respectively, is derived. It is then shown that for all elements in the uncertainty class this choice of likelihood ratio guarantees the exponential convergence of the aforementioned Chernoff bounds to zero as the number of observations or the length of the observation interval increases.     

A generalized method for encoding and decoding run-length-limited binary sequences (Corresp.)

Many modulation systems used in magnetic and optical recording are based on binary run-length-limited codes. We generalize the concept ofdk-limited sequences of length n introduced by Tang and Bald by imposing constraints on the maximum number of consecutive zeros at the beginning and the end of the sequences. It is shown that the encoding and decoding procedures are similar to those of Tang and Bald. The additional constraints allow a more efficient merging of the sequences. We demonstrate two constructions of run-length-limited codes with merging rules of increasing complexity and efficiency and compare them to Tang and Bahl's method.