Edward C. Posner

A new clustering algorithm applicable to multispectral and polarimetric SAR images

The authors applied a scale-space clustering algorithm to the classification of a multispectral and polarimetric SAR image of an agricultural site. After the initial polarimetric and radiometric calibration and noise cancellation, a 12-dimensional feature vector for each pixel was extracted from the scattering matrix. The clustering algorithm partitioned a set of unlabeled feature vectors from 13 selected sites, each site corresponding to a distinct crop, into 13 clusters without any supervision. The cluster parameters were then used to classify the whole image. The classification map is much less noisy and more accurate than those obtained by hierarchical rules. Starting with every point as a cluster, the algorithm works by melting the system to produce a tree of clusters in the scale space. It can cluster data in any multidimensional space and its insensitive to variability in cluster densities, sizes and ellipsoidal shapes. This algorithm, more powerful than existing ones, may be useful for remote sensing for land use. >

The capacity of the photon counting channel

Previous work has shown that the capacity of the single-mode photon-counting channel in the region in which quantum effects are most pronounced is 1/(kT \ln 2) bit/J. Here T is the quantum noise temperature, and k is Boltzmanns constant. However, to achieve this, the number of photons per second must be very low, so this does not determine the capacity of the average power-limited photon channel in bits per second. Here the previous work is extended and the capacity is determined in bits per second. This includes a determination of the optimum counting time. The capacity in bits per second is for low T asymptotic to P_{s}/(kT \ln 2) , where P_{s} is the average signal power. This is high enough to suggest that photon counting be seriously considered for applications such as a deep space to near Earth link. Some related problems are also considered including a peak power limitation.

Optimum cyclic redundancy codes for noisy channels (Corresp.)

Binary cyclic redundancy codes for feedback communication over noisy digital links are considered. The standard 16-bit ADCCPt polynomial is designed for digital links that already have a low input bit error probability. For file transfer between personal computers over telephone circuits, the quality of the resulting digital circuit may be much lower. This leads to the consideration of 3-byte (24-bit) and 4-byte (32-bit) polynomials. Generator polynomials of a certain class are found that have minimum weight and yet achieve the bound on minimum distance for arbitrary codes. Particular polynomials for 24-bit and 32-bit redundancies are exhibited, of weight and distance 6 in the 24-bit case and weight 10 and distance 8 in the 32-bit case.

Systematic Statistics Used for Data Compression in Space Telemetry

Abstract The need for data compression, a consequence of the demands made on the telemetry system of a space vehicle, prompts consideration of the use of sample quantiles in estimating population parameters and obtaining tests of goodness of fit for large samples. In this paper optimal unbiased estimators of the mean and standard deviation are given using up to twenty quantiles when the parent population is normal. Moreover, the estimators are relatively insensitive to deviations from normality. A distribution-free goodness-of-fit test is presented based on the sum of the squares of four quantiles after an orthogonal transformation to independent normal deviates. If a frequency function is of the form f(x; p) = pf 1(x) + (1 - p) f 2(x), 0 < p < 1, where f 1 and f 2 are normal frequency functions, the distribution is likely to be bimodal. Another goodness-of-fit test is obtained using four quantiles, which is likely to have considerable power with a null hypothesis of normality and the alternative hypothes...

Rook domains, Latin squares, affine planes, and error-distributing codes

A problem originally suggested in the context of genetic coding leads naturally to the concept of {\em rook packing} and {\em error-distributing codes}. It is shown how various concepts in the theory of Latin squares, and also in coding theory, are best expressed in the form of questions about the placing of rooks on k -dimensional hyperchessboards of side n . A new species of combinatorial design suggested by this is the concept of {\em optimal coloring}. It is shown that the optimal colorings in certain cases correspond to duals of desarguian projective planes. Light is thereby shed on the problems of the existence of both finite projective planes and close-packed single-error-correcting codes. In particular, the existence of a certain close-packed nonbinary single-error-correcting code, listed by Golay as the first unknown case, has been ruled out by a well-known result concerning Latin squares.

Optimal search procedures

This paper sets up a restricted class of search procedures for a satellite lost in a region of the sky. The satellite must be found by a radar search. The procedures under consideration allow the use of a preliminary search, which may be done with a wider beam than is required for the final search. The purpose of the preliminary search is to obtain a ranking of the various portions of the sky, so that the final search can examine the more likely regions of the sky first. It is shown that a preliminary search can reduce the expected search time, with no matter how wide a beam it is carried out. It is also shown that the preliminary search with the narrowest possible beam is best.

The Application of Extreme-Value Theory to Error-Free Cornrnunication

This article gives an application of Gumbels extreme-value theory to the problem of the estimation of low error probabilities in certain types of communications receivers, for the purpose of rejecting receivers having unacceptably high error rates. The systems considered all involve threshold detectors in a binary system. Thus, the receiver calls a received symbol a “0” if and only if a certain detected voltage falls below a certain value; otherwise, the symbol is called a “1”. The maximum of a run of a large number of successive independent samples of voltage is taken, and these maxima have approximately a Gumbel distribution. A large number of these maxima themselves are taken, and the two parameters of the Gumbel distribution are thereby estimated using large sample theory. These two parameters in turn allow the estimation of error probability. The variance of the estimate is found, as well as a confidence interval. In addition, the savings to be obtained using the Gumbel method, as opposed to the sim...

Call setup strategy tradeoffs for universal digital portable communications

Abstract This paper proposes and analyzes a criterion for database update frequency in universal portable digital communication (UPDC), based on the rate of diffusion of mobile subscribers. More frequent updates reduce the search area, which reduces expected paging time and paging traffic at the expense of database size.

The capacity of digital links in tandem

Suppose we have L digital links in tandem. Between successive links we have a repeater. The links are each white Gaussian channels with no bandwidth constraint. The repeater may either be a {\em binary repeater}, which sends on each bit separately having made a binary decision on each, or a {\em Shannon repeater}, which perfectly reproduces at one end the bits that were transmitted at the other end of the link. What is the loss in capacity if we use only binary repeaters and code for the entire L links at the transmit end? For large L , the capacity drops by a factor asymptotic to In L , and the normalized optimum time T per symbol T_{\opt}^{L} is also asymptotic to \ln L . Arbitrarily short L gives 0 capacity for L > 1 . More precise asymptotic results are obtained and compared with computed numerical values. These results show when it pays to code each link separately in digital data transmission.

Deep space communication - Past, present, and future

This paper reviews the progress made in deep space communication from its beginnings until now, describes the development and applications of NASAs Deep Space Network, and indicates directions for the future. Limiting factors in deep space communication are examined using the upcoming Voyager encounter with Uranus, centered on the downlink telemetry from spacecraft to earth, as an example. A link calculation for Voyager at Uranus over Australia is exhibited. Seven basic deep space communication functions are discussed, and technical aspects of spacecraft communication equipment, ground antennas, and ground electronics and processing are considered.