In this work, we consider a large-scale geographic area populated by tiny sensors and some more powerful devices called actors, authorized to organize the sensors in their vicinity into short-lived, actor-centric sensor networks. The tiny sensors run on miniature nonrechargeable batteries, are anonymous, and are unaware of their location. The sensors differ in their ability to dynamically alter their sleep times. Indeed, the periodic sensors have sleep periods of predefined lengths, established at fabrication time; by contrast, the free sensors can dynamically alter their sleep periods, under program control. The main contribution of this work is to propose an energy-efficient location training protocol for heterogeneous actor-centric sensor networks where the sensors acquire coarse-grain location awareness with respect to the actor in their vicinity. Our theoretical analysis, confirmed by experimental evaluation, shows that the proposed protocol outperforms the best previously known location training protocols in terms of the number of sleep/awake transitions, overall sensor awake time, and energy consumption.

Scalable energy-efficient training protocols are proposed for wireless networks consisting of sensors and a single actor, where the sensors are initially anonymous and unaware of their location. The protocols are based on an intuitive coordinate system imposed onto the deployment area, which partitions the sensors into clusters. The protocols are asynchronous, in the sense that the sensors wake up for the first time at random, then alternate between sleep and awake periods both of fixed length, and no explicit synchronization is performed between them and the actor. Theoretical properties are stated under which the training of all the sensors is possible. Moreover, both worst-case and average case analyses of the performance, as well as an experimental evaluation, are presented showing that the protocols are lightweight and flexible.

A new method is proposed for converting residue integers into a mixed radix notation. The method is based upon a modified formulation of the Chinese Remainder Theorem, and permits both conventional logic and look-up table implementations. Moreover, it represents the first method enabling optimal, residue-to-weighted system, asymptotic conversion time. To prove this, a constructive VLSI design has been devised, exhibiting time O(log s), where s is the total number of input bits. If compared with the existing mixed radix converting techniques, the method proposed considerably enhances the conversion time. To conclude, it is shown that, at the present state of the technology, practical ECL IC's implementation achieve 35–40 ns conversion times with RAMs and 60–70 ns with logic circuitry for dynamic ranges up to 300 bits.

Hybrid number systems (HNSs) represent a natural generalisation of weighted and residue number systems. In HNSs, an integer is represented by using both weighted and residue notations; their mathematical properties, which have been investigated in depth, are strongly dependent on the ratio of the residue to the weighted range of the representation. It is apparent that varying the residue-to-weighted-range ratio should enable us to optimise the mathematical performances of these systems. This paper shows that adding flexibility to hybrid systems is very simple. A general procedure is proposed whose complexity is the same as the well-known mixed radix converting algorithm. A VLSI architecture is presented and its area-time performances are evaluated.

In this paper a fast procedure is presented to fairly interpolate a given set of points, which is mainly based on the use of table look-up techniques. Storage amounts required can be easily supplied by present memories technology. Though our procedure can be applied to any interpolation method, it is well suited for a spline, using an angle as a parameter, which was defined by the authors in a previous paper. Benefits and limits of the procedure are discussed and several examples of its behaviour are given.

The idea of adding a magnitude index to the residue representation of numbers is reconsidered. The range of a given residue number system is supposed to be divided into intervals of equal width, and the magnitude index of a number X is defined as an integer locating X into one of such intervals. It is shown that the redundancy implied by the use of the magnitude index allows error detection or correction, and the redundancy requirements to detect or correct single residue digit errors are the same as in redundant residue number systems and in product codes in residue number systems. In addition, these codes allow detection of any error affecting the residue representation, provided that the magnitude of the error exceeds a given threshold, and, whenever an error is detected, it is possible to replace the wrong number with an approximation of the correct number.

Two classes of arithmetic codes constructed in residue number systems are considered, and decoding algorithms based on the convergents of continued fractions are presented. The advantages of the proposed algorithms over those previously known are discussed.

The problem of automatic fault diagnosis of systems decomposed into a number of interconnected units is considered by using a simplified version of the diagnostic model introduced by Preparata et al. The model used in this paper is supposed to be a realistic representation of systems where each unit has a considerable computational capability. For any system of n units whose set of testing links is given, necessary and sufficient conditions for t-diagnosability are presented in both cases of one-step diagnosis and diagnosis with repair, and it is shown that the procedure for diagnosis with repair has very small complexity. The problem of optimal assignment of testing links in order to achieve a given diagnosability is also considered and classes of optimal t-diagnosable systems are presented for arbitrary values of t in both cases of one-step diagnosis and diagnosis with repair.

The arithmetic error detecting and correcting capabilities of product (AN) codes in residue number systems (RNS) are described. The redundancy necessary and sufficient to allow single residue digit error detection or correction is determined, under the hypothesis that the error affects either an arbitrary legitimate number or a number in overflow. It is shown that single-bit errors are also correctable, provided that the residue digits are conveniently encoded. Two different approaches to this problem are discussed. Simple procedures for error detection and correction are presented, and it is shown that the additive overflow detection is a by-product of such procedures. Proofs and examples are given.

The error correcting properties of the redundant residue number systems (RNS) are investigated through a more natural a approach than was previously known. The necessary and sufficient condition for the correction of a given error affecting a single residue digit of any legitimate number in an RRNS is determined. The minimal redundancy allowing the correction of the whole class of the single residue digit errors is derived and an efficienit procedure for error correction is given. Moreover, it is shown that a smaller redundancy and a single redundant modulus may allow the correction of certain important subclasses of single residue digit errors, e.g., the set of errors affecting a single bit in the code. Examples are given.