786 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 1~24, NO. 6, NOVEMBER 1978

of channel coding, and there is one lecture apiece on source coding Introduction to Chuuumieations Engineering, R. Gagliardi (New York: algorithms, decoder computational effort, degraded broadcast chan- Wiley, 1978, xi + 508 pp., $26.50). To be reviewed. nels, and a “logical approach to information theory” that “aims at being a generalization of the Kolmogorov algorithmic approach.” Digital Image Proceaslng, R. C. Gonzalez, and P. Wintz (Reading, MA:

Lectures on Linear Least-Squares Estlmatlon, T. Kailath (New York: Addison-Wesley, 1977, xvi+431 pp., $29.50 hardcover, $19.50 soft cover). To be reviewed.

Springer, 1976, 169 pp.). A version of lectures presented at a 1972 summer school sponsored Dlgltal Image processing W. K. Pratt (New York: Wiley, 1978, x+750

by CISM, Udine, Italy. Presumes no prior background in the subject. pp., $33.00). To be reviewed.

Dissertation Abstracts

Ming Un Clumg, “Rate-distortion with a fully informed decoder and partially informed encoder,” Ph.D., School Elec. Eng., Cornell Univ., Ithaca, NY June 1978. Advisor: T. Berger.

This dissertation is addressed to the following problem in multitermi- nal source coding. The discrete memoryless source (DMS) {X,) is to be encoded for transmission to a destination at an information rate of R, bit/symbol. Side information is available at said destination in the form of another DMS ( Y,}. The joint distribution of X, and Y, is denoted by P and does not depend on k. Moreover, information about { Yk} may be supplied to the encoder at a rate of R bit/symbol. This is a generaliza- tion of the rate-distortion problem of Wyner and Ziv in which no side information is available at the encoder (R = 0).

Let R,(d,R) denote the least value of Rx that suffices to permit reconstruction of {X,} at the destination with fidelity d as assessed by means of a memoryless distortion measure p(x,$. By means of a random coding technique incorporating the concept of strongly jointly typical sequences, an upper bound to R,(d, R) is proved. A lower bound is established, too, by using information-theoretic identities and inequali- ties. Both bounds have the so-called “single-letter” or “instantaneous” form, which is the only form that most information theorists consider acceptable. The bounds are shown to be nontrivial in the sense that the upper bound is less than or equal to the Wyner-Ziv rate-distortion function, and the lower bound is greater than or equal to the conditional rate-distortion function. For R=O, the upper bound reduces to the solution provided by Wyner and Ziv, and for R >H( Y/X), the upper and the lower bounds both equal the conditional rate-distortion func- tion Rxlr(d). Another upper bound, corresponding to optimum time sharing of the Wyner-Ziv and conditional rate-distortion modes, also is introduced and is compared to the other bounds.

Alain Crolotte, “Memory versus error tradeoffs in question-answering systems,” Ph.D., School Eng. Appl. Sci., Univ. California, Los Angeles, CA, 1978.

It has often been conjectured that systems can improve their perfor- mance if they parallel man’s ability to tolerate occasional errors. The purpose of this dissertation is to test this hypothesis in the framework of question-answering (QA) systems with storage requirements as a com- plexity measure.

A QA system is an inductive device which answers queries from a given set about data sets from a specific ensemble. Such systems are viewed here as communication channels. This allows the use of a well-established mathematical framework: Shannon’s rate-distortion theory.

For a QA system, Shannon’s rate-distortion function R(D) is the minimum amount of memory to provide to the system in order to

achieve an average distortion less than D (the distortion can be, for example, the average proportion of erroneous answers produced by the system).

The ability of the system to convert an amount D of error into a saving in memory is measured by the ratio R(D)/R(O). A system will be called elastic if this ratio goes to zero as M, the size of the data set ensemble, tends to infinity. The main task of this dissertation is to determine what qualities of a QA system render it elastic.

Since it is not possible, in general, to find the analytical expression of R(D), analytically tractable bounds to R(D) are provided. These bounds fall into two categories:

0 absolute bounds depending only on the parameters of the system and the distance metric used;

0 general bounds depending on the distortion matrix as well.

The asymptotic behavior of these bounds is found, and conditions for elasticity are established. These conditions are then applied to simple yet typical QA systems.

Carol A. Nimik, “Measures of congestion for computer communication networks,” Ph.D., Dep. Elec. Eng., State Univ. New York at Buffalo, Amherst, NY, April 1978. Advisor: D. Kazakos.

The problem in computer communication networks that is most dif- ficult to solve is the reduction in throughput, reliability, quality of operation, and survivability due to local and global congestion. Present combinatorial congestion measures developed for the Advanced Re- search Projects Agency Network (ARPANET), European networks, and general network models do not provide methods which measure delay through the levels of the hierarchy of the network. The objective of this research, therefore, is to determine a number of general analytical measures which can be implemented in congestion control schemes for different topological network configurations. The delay measures devel- oped have their basis in the disciplines of queueing theory, advanced theory of stochastic processes, probabilistic automata theory, and graph theory. Application of the measures is demonstrated on three topologies, a single node, two nodes in tandem, and a hierarchical network. User throughput, an end-to-end path delay measure, is directly influenced by these measures.

A lower and upper bound solution of the mean waiting time for a single node GZ/ G/ 1 queue is derived by a quantization approach. Then, this basic measure is extended via a probabilistic automata model to obtain a point-to-point waiting time measure in a single-node, a two- node tandem, and a hierarchical network configuration containing com- munication ports at the inputs and outputs of the nodes. The mathemati- cal structure is the combination of the probability transition matrices which represents the intranode port and buffer transitions of a node and