It has been recently discovered that complementary graph entropy characterizes (and offers new insights into) the minimum asymptotic rate for zero-error source coding with decoder side information. This paper presents new results that build on and complement this discovery. Specifically, i) previously unknown subadditivity properties of complementary graph entropy are derived, and ii) zero-error coding rates are characterized in terms of complementary graph entropy for two multiterminal coding scenarios. For both scenarios, the rate characterization implies no rate loss relative to point-to-point source coding.

A proxy signature scheme allows one user to delegate his/her signing capability to another user called a proxy signer in such a way that the latter can sign messages on behalf of the the former. After verification the verifier is convinced of the original signer's agreement on the signed message. We have come up with a scheme to control delegation of financial power to a proxy signer. The scheme satisfies the basic requirements of a secure proxy signature scheme. Using our scheme the proxy signer will be able to submit an e-cheque for only the amount he is entitled to by the original signer. Any cheating by the original signer or the proxy signer is identified by the verifier i.e. the bank. We have considered Forgery by the original signer, Impersonating and framing attack to prove the security of our scheme. Any discrete log based signature scheme can be used to sign the messages. Here we use the digital signature algorithm (DSA).

This paper investigates the relationship between rate-distortion theory and efficient content-based data retrieval from high-dimensional databases. We consider database design as the encoding of a data object sequence, and retrieval from the database as the decoding of the sequence using side information (i.e., the query) available only at the decoder. We show that, in this setting, the optimal asymptotic tradeoff between the search time R/sub s/ (bits per data object read from the storage device) and the expected search accuracy D/sub s/ (relevance of the retrieved data set) is given by the Wyner-Ziv solution with a side-information-dependent distortion measure. Moreover, the data indexing and retrieval problem is, in general, inseparable from the data compression problem. Data items selected by the search procedure, which can be stored in the disk with a limited total rate of R/sub r/ /spl ges/ R/sub s/, need to be presented at a prescribed expected reconstruction quality D/sub r/. This is, hence, a problem of scalable source coding or successive refinement, albeit with differing layer distortion measures to quantify search and reconstruction quality, respectively. We derive a single-letter characterization of all achievable quadruples {R/sub s/,R/sub r/,D/sub s/,D/sub r/}, and prove conditions for "successive refinability" without rate loss. Finally, we show that the special case D/sub s/=D/sub r/=0 is nontrivial and of practical interest in this context, as it can impose "acceptable" search and reconstruction qualities for each individual data item and for the entire query space with high probability, in contradistinction with standard average distortion requirements. The region of achievable {R/sub s/,R/sub r/} is obtained by adapting Rimoldi's characterization to a new regular scalable coding problem.

The design of vector quantizers for diversity-based communication over two or more channels of possibly differing capacities and failure probabilities, is considered. The crucial dependence of current design techniques on initialization, especially of index assignment, is well recognized. Instead, we propose to pursue a deterministic annealing approach which is independent of initialization, does not assume any prior knowledge of the source density, and avoids many poor local minima of the cost surface. The approach consists of iterative optimization of a random encoder at gradually decreasing levels of randomness as measured by the Shannon entropy. At the limit of zero entropy, a hard multiple description (MD) quantizer is obtained. This process is directly analogous to annealing processes in statistical physics. Via an alternative derivation, we show that it may also be interpreted as approximating the minimum rate sums among points on the convex hull of the MD achievable rate-distortion region of El Gamal and Cover, subject to constraints on the sizes of the reproduction alphabets. To illustrate the potential of our approach, we present simulation results that show substantial performance gains over existing design techniques.

Let (X,Y) be a pair of random variables distributed over a finite product set V/spl times/W according to a probability distribution P(x,y). The following source coding problem is considered: the encoder knows X, while the decoder knows Y and wants to learn X without error. The minimum zero-error asymptotic rate of transmission is shown to be the complementary graph entropy of an associated graph. Thus, previous results in the literature provide upper and lower bounds for this minimum rate (further, these bounds are tight for the important class of perfect graphs). The algorithmic aspects of instantaneous code design are considered next. It is shown that optimal code design is NP-hard. An optimal code design algorithm is derived. Polynomial-time suboptimal algorithms are also presented, and their average and worst case performance guarantees are established.

The problem of separate zero-error coding of correlated sources is considered. Inner and outer single-letter bounds are established for the achievable rate region, and conditions for their coincidence are investigated. It is shown that successive encoding combined with time sharing is not always an optimal coding strategy. Conditions for its optimality are derived. The inner bound to the achievable rate region follows as a special case of the single-letter characterization of a generalized zero-error multiterminal rate-distortion problem. The applications of this characterization to a problem of remote computing are also explored. Other results include (i) a product-space characterization of the achievable rates, (ii) bounds for finite block length, and (iii) asymptotic fixed-length rates.

Let finite source and reproduction alphabets X and Y and a distortion measure d: X/spl times/Y/spl rarr/[0,/spl infin/) be given. We study the minimum asymptotic rate required to describe a source distributed over X within a (given) distortion threshold D at every sample. The problem is hence a min-max problem, and the distortion measure is extended to vectors as follows: for x/sup n//spl isin/X/sup n/, y/sup n//spl isin/Y/sup n/, d(x/sup n/, y/sup n/)=max/sub i/d(x/sub i/, y/sub i/). In the graph-theoretic formulation we introduce, a code for the problem is a dominating set of an equivalent distortion graph. We introduce a linear programming lower bound for the minimum dominating set size of an arbitrary graph, and show that this bound is also the minimum asymptotic rate required for the corresponding source. Turning then to the optimality of scalar coding, we show that scalar codes are asymptotically optimal if the underlying graph is either an interval graph or a tree.