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.>

Describes application of scale-space clustering to the classification of a multispectral and polarimetric SAR image of an agricultural site. After polarimetric and radiometric calibration and noise cancellation, the authors extracted a 12-dimensional feature vector for each pixel from the scattering matrix. The algorithm was able to partition without supervision a set of unlabeled vectors from 13 selected sites, each site corresponding to a distinct crop, into 13 clusters. 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. The algorithm can handle variabilities in cluster densities, cluster sizes and ellipsoidal shapes.>

Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory storesn-tuple of\pm 1's. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products ofmfundamental memories, one hopes to be able to recover a certain one of themmemories by using an initialn-tuple probe vector less than a Hamming distancen/2away from the fundamental memory. Ifmfundamental memories are chosen at random, the maximum asympotic value ofmin order that most of themoriginal memories are exactly recoverable isn/(2 \log n). With the added restriction that every one of themfundamental memories be recoverable exactly,mcan be no more thann/(4 \log n)asymptotically asnapproaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory capacity problem is closely related to the capacity of the quantized Gaussian channel.

This note considers codes for computer file transfer protocols when only upper-case ASCII characters are used as control characters. Such a restriction may be necessary to avoid dependence on unique machine features and to promote portability. If ten control functions are needed, a number used in a typical sufficiently rich protocol, we seek a subset of ten upper-case ASCII characters with good distance properties. The control functions form themselves naturally into three groups. Recognizing that only even distances can occur, we wish to make the intragroup minimum distances as large as possible, and the number of control characters having distance 2 as small as possible. We find the optimum solution to the above problem and an assignment that attains the optimum. The codes are essentially unique.

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.

Suppose we haveLdigital 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 largeL, the capacity drops by a factor asymptotic to InL, and the normalized optimum timeTper symbolT_{\opt}^{L}is also asymptotic to\ln L. Arbitrarily shortLgives0capacity forL > 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.

A strategy for data acquisition from a very distant spacecraft is presented, when the system performance can be severely degraded by the earth's weather due to the high microwave frequency being used. Two cases are considered, one in which there is a certain minimum data rate to be maintained and one in which there is not. The goal is to maximize expected data return, where we assume that there are always new data, or a backlog of old data, that can be sent if conditions are favorable. When there is no minimum rate to be maintained, the optimum strategy is typically the greedy strategy, which always transmits at that single rate which maximizes the expected data returned. If there is a minimum data rate which we strive to maintain even in adverse conditions, the optimum strategy transmits simultaneously at the minimum or base data rate and typically at a bonus data rate. We use a coding system designed for the bandwidthconstrained degraded broadcast channel. The optimum version of this system can, under realistic assumptions, save on the order of 5 dB over the conservative strategy of just transmitting at a single lower data rate.

The capacity region for the discrete memoryless multiple-access channel without time synchronization at the transmitters and receivers is shown to be the same as the known capacity region for the ordinary multiple-access channel. The proof utilizes time sharing of two optimal codes for the ordinary multiple-access channel and uses maximum likelihood decoding over shifts of the hypothesized transmitter words.

Previous work has shown that the capacity of the single-mode photon-counting channel in the region in which quantum effects are most pronounced is1/(kT \ln 2)bit/J. HereTis the quantum noise temperature, andkis Boltzmann's 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 lowTasymptotic toP_{s}/(kT \ln 2), whereP_{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.

This paper proves that there exists a fixed random coding Strategy for block coding a memoryless information source to achieve the absolute epsilon entropy of the source. That is, the strategy can be chosen independent of the block length. The principal new tool is an easy result on the semicontinuity of the relative entropy functional of one probability distribution with respect to another. The theorem generalizes a result from rate-distortion theory to the "zero-infinity" case.

Given a finite probability spaceXand an a priori distributionP = P(0) = \{p_{i}(0)\}, exact expressions for minimum search time (to determine the one and only one nonzero mean process) are derived. Only one pointimay be observed at a given time, in contrast to the more standard decision theory problem where all n processes are observed simultaneously. The problem is formulated in continuous time, as a limiting case of discrete-time hypothesis tests. The performance of the optimal strategy is shown to be far superior to the performance of some standard strategies.

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 onk-dimensional hyperchessboards of siden. 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.

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.