A fast algorithm for the Fourier transform over finite fields andits VLSI implementation

The Fourier transform over finite fields is mainly required in the encoding and decoding of Reed-Solomon and BCH codes. An algorithm for computing the Fourier transform over any finite field GF(p^m) is introduced. It requires only O(n(log n)²/4) additions and the same number of multiplications for an n-point transform and allows in some fields a further reduction of the number of multiplications to O(n log n). Because of its highly regular structure, this algorithm can be easily implementation by VLSI technology     

High-speed Ga0.47In0.53As/InP infra-redSchottky-barrier photodiodes

The authors report a new high-speed InP-based Ga_1-xIn _xAs infra-red Schottky-barrier photodiode. The photodiodes were fabricated on both p- and n-GaInAs epilayers using Schottky barrier height enhancement technology. The response speed was measured by the impulse response and autocorrelation method; the risetimes of 85 ps for p-GaInAs and 180 ps for n-GaInAs photodiodes were obtained, which correspond to the 3 dB cutoff frequency of 2-4 GHz. The intrinsic response speed was 12 GHz for n-GaInAs and 18 GHz for p-GaInAs photodiodes based on SPICE simulation with measured device parameters. The photodiodes had the responsivity as high as 0.55 A/W and the quantum efficiency of up to 45% at 1.3-1.6 μm without antireflection coating     

Tissue dielectric measurement using an interstitial dipole antenna

The purpose of this study was to develop a technique to measure the dielectric properties of biological tissues with an interstitial dipole antenna based upon previous efforts for open-ended coaxial probes. The primary motivation for this technique is to facilitate treatment monitoring during microwave tumor ablation by utilizing the heating antenna without additional intervention or interruption of the treatment. The complex permittivity of a tissue volume surrounding the antenna was calculated from reflection coefficients measured after high-temperature microwave heating by using a rational function model of the antenna's input admittance. Three referencing liquids were needed for measurement calibration. The dielectric measurement technique was validated ex vivo in normal and ablated bovine livers. Relative permittivity and effective conductivity were lower in the ablation zone when compared to normal tissue, consistent with previous results. The dipole technique demonstrated a mean 10% difference of permittivity values when compared to open-ended coaxial cable measurements in the frequency range of 0.5-20 GHz. Variability in measured permittivities could be smoothed by fitting to a Cole-Cole dispersion model. Further development of this technique may facilitate real-time monitoring of microwave ablation treatments through the treatment applicator.     

Frequency-hopping code sequence designs having large linear span

In frequency-hopping spread-spectrum multiple-access communication systems, it is desirable to use sets of hopping patterns that, in addition to having good Hamming correlation properties and large period, are also derived from sequences having large linear span. Here, two such frequency hopping code sequence designs that are based on generalized bent functions and generalized bent sequences are presented. The Hamming correlation properties of the designs are optimal in the first case and close to optimal in the second. In terms of the alphabet size p (required to be prime in both cases), the period and family size of the two designs are given by (p², p) and (p ⁿ, p^n/2+1) (n an even integer), respectively. The finite field sequences underlying the patterns in the first design have linear span exceeding p, whereas still larger linear spans (when compared to the sequence period) can be obtained using the second design method     

Calculation of the binomial survivor function [reliabilityapplications]

A method is presented for calculating the binomial SF (cumulative binomial distribution), binfc(k;p,n), especially for a large n, beyond the range of existing tables, where conventional computer programs fail because of underflow and overflow, and Gaussian or Poisson approximations yield insufficient accuracy for the purpose at hand. This method is used to calculate and sum the individual binomial terms while using multiplication factors to avoid underflow; the factors are then divided out of the partial sum whenever it has the potential to overflow. A computer program uses this technique to calculate the binomial SF for arbitrary inputs of k, p, and n. Two other algorithms are presented to determine the value of p needed to yield a specified SF for given values of k and n and calculate the value where p=SF for a given k and n. Reliability applications of each algorithm/program are given, e.g. the value of p needed to achieve a stated k-out-of-n :G system reliability and the value of p for which k -out-of-n:G system reliability equals p     

On the cutoff point for pairwise enabling in multiple accesssystems

Let p⁰ be the minimum Bernoulli probability for which pairwise enabling is an optimal group testing algorithm under a Bernoulli arrival sequence model. In a previous work, it was shown that 0.430⩽p⁰⩽0.568 for unbounded Bernoulli arrival sequences, based on the threshold probabilities at which certain triple enabling algorithms (operating with and without the aid of a helpful genie, respectively) become more efficient. By deriving constructive results using the powerful but seemingly nonconstructive upper-bounding technique introduced by N.A. Mikhailov and B.S. Tsybakov (1981), the author sharpens this result by proving that p⁰ ⩽0.5 for unbounded arrival sequences, and that p⁰≈0.545 in the finite arrival sequence model recently studied by F.K. Hwang and X.M. Chang (1987). The present results for unbounded arrival sequences also extend to the reservation schemes considered by Hwang and Chang, where it is now shown that 0.386⩽p⁰_I⩽0.387 under the intermediate reservation model and 0.436⩽p⁰_G⩽1/√3 under the Gudjohnsen reservation model, respectively     

An updating algorithm for subspace tracking

In certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components. The usual tool for doing this is the singular value decomposition. However, the singular value decomposition has the drawback that it requires O(p³) operations to recompute when a new sample arrives. It is shown that a different decomposition, called the URV decomposition, is equally effective in exhibiting the null space and can be updated in O( p²) time. The updating technique can be run on a linear array of p processors in O(p) time     

Dynamic control and accuracy of thepi-persistent protocol using channel feedback

The p_i-persistent protocol is based on a probabilistic scheduling mechanism (see Mukherjee and Meditch, 1988). The authors further develop the protocol to make it easily implementable, by allowing it to be sensitive to changing load conditions. They study various properties of a simple algorithm which stations execute independently by using channel feedback information. This results in a fully distributed control mechanism that continuously adjusts the station probabilities p_i at their proper levels as governed by the offered traffic. An extensive simulation model has been developed to study properties of this control mechanism such as p_i settling time and accuracy, behavior under step changes in traffic load, effect of injection of additional packets, and effect of various parameters associated with the underlying algorithm. These experiments indicate that this algorithm is suitable for implementing the protocol     

Optical orthogonal codes-new bounds and an optimal construction

A technique for constructing optimal OOCs (optical orthogonal codes) is presented. It provides the only known family of optimal (with respect to family size) OOCs having λ=2. The parameters (n ,ω,λ) are respectively (p^2m-1, p^m+1,2), where p is any prime and the family size is p^m-2. Three distinct upper bounds on the size of an OOC are presented that, for many values of the parameter set (n,ω,λ), improve upon the tightest previously known bound     

A Simple Coaxial Exposure Cell for Biological Substances

A coaxial cell suitable for exposure of biological substances to electromagnetic fields in the frequency range from dc to 100 MHz is described. The cell provides uniform electric field throughout the exposed sample, requires a relatively small volume of the sample (typically below 1 ml), and allows for convenient control of the sample temperature.     

Theoretical and experimental study of measurement of microwavepermittivity using open ended elliptical coaxial probes

In this paper, a new kind of coaxial probe for measurement of microwave permittivity-an open-ended elliptical aperture-is studied from theoretical and experimental viewpoints. Calculated results are discussed and compared with experimental values. Wideband measurements of the dielectric constants of liquids are performed by using this kind of needle type probe. Both theory and experiment show that open-ended elliptical coaxial probes can be successfully used in wideband dielectric constant measurements with the advantage of increased sensitivity, especially at low frequencies. Moreover, this kind of probe can easily be fitted into gels and living tissues. These features are very important in biological applications both for measurements and microwave radiation treatment     

A new family of optical code sequences for use in spread-spectrumfiber-optic local area networks

The problem of the algebraic construction of a particular family of optical codes for use in code-division multiple-access (CDMA) fiber-optic local area networks (LANs) is treated. The conditions that the code families have to satisfy when used in such systems are reviewed. The new codes are called quadratic congruence codes, and the construction of the corresponding sequences is based on the number-theoretic concept of quadratic congruences. It is shown that p-1 codes exist for every odd prime p and can serve as many as p-1 different users in the CDMA fiber-optic system. The codes belong to the family of optical orthogonal codes, their auto- and cross-correlation properties are established, and their performance is compared to that of the previous optical codes. Examples of the codes and examples of their auto- and cross-correlation functions are given     

On the competitive optimality of Huffman codes

Let X be a discrete random variable drawn according to a probability mass function p(x), and suppose p(x), is dyadic, i.e., log(1/p(x)) is an integer for each x. It is shown that the binary code length assignment l(x)=log(1/p(x)) dominates any other uniquely decodable assignment l'(x) in expected length in the sense that El(X)<El'(X), indicating optimality in long run performance (which is well known), and competitively dominates l'(x), in the sense that Pr{ l (X)<l'(X)}>Pr{l ( X)>l'(X)}, which indicates l is also optimal in the short run. In general, if p is not dyadic then l=[log 1/p] dominates l'+1 in expected length and competitivity dominates l'+1, where l' is any other uniquely decodable code     

The pi-persistent protocol for unidirectionalbroadcast bus networks

A protocol for multiaccess communication over unidirectional bus networks is proposed, and its performance capabilities are determined. Under this protocol, time is slotted with a slot equaling a packet's transmission time. A station with a packet to send persists in transmitting its packet in an empty slot with probability p_i until it is successful. Three criteria for fairness in selection of the p_i are modeled using Markov chains, which are solved to obtain the proper p_i that satisfy each fairness criterion. Unlike previous studies of unidirectional bus networks, stations are allowed to buffer more than one packet. The average packet delay for this protocol is bounded, and the maximum achievable throughput approaches unity with increasing buffer size. Further, the protocol provides better delay versus throughput behavior for fixed packet lengths than previous round-robin schemes, its performance is insensitive to bus characteristics, and it appears to be particularly well suited for fiber-optic network applications requiring long distances and high bandwidths. Simulation results that confirm the predicted performance are included     

A fast signature scheme based on congruential polynomial operations

A novel digital signature scheme is proposed in which the computation time is much shorter than that of the Rivest-Shamir-Adelman (RSA) scheme, while the key length and signature length are comparable to those for the RSA scheme. Moreover, the proposed scheme can be implemented easily and is, therefore, more practical for many digital signature applications. The scheme is based on congruential polynomial operations whose degrees are more than three. The secret key consists of two large prime numbers, p and q, and the public key is their product, n=p²q. The security of this scheme depends on the difficulty of factorizing the number n. Variations using the number of zeros succeeding the significant bit are also proposed     

Parallel testing of parametric faults in a three-dimensionaldynamic random-access memory

A testable design of dynamic random-access memory (DRAM) architecture which allows one to access multiple cells in a word line simultaneously is presented. The technique utilizes the two-dimensional (2-D) organization of the DRAM and the resulting speedup of the conventional algorithm is considerable. The failure mechanism in the three-dimensional (3-D) DRAM with trench-type capacitor is specifically investigated. As opposed to the earlier approaches for testing parametric faults that used sliding diagonal-type tests with O(n^3/2) complexity, the algorithms discussed here are different and have O(√n/p) complexity, where p is the number of subarrays within the DRAM chip. These algorithms can be applied externally from the chip and also they can be easily generated for built-in self-test applications     

A storage-efficient method for solving banded Toeplitz systems

A method is presented for solving the banded Toeplitz system Tx=y by decomposing T into its asymptotic upper and lower triangular factors (which are banded and Toeplitz) and a rank-p correction matrix, where p is the bandwidth of T. This way of representing T requires only O(p²) words of storage and allows computation of x in O(2Np) operations. A similar method is presented for the case in which T is bi-infinite and y is zero outside a finite region     

Phase tree: a periodic, fractional flux quantum vernier forhigh-speed interpolation of analog-to-digital converters

A Josephson junction circuit that can rapidly track and record a magnetic flux signal to a small binary fraction of the flux quantum is proposed. This so-called phase tree circuit behaves periodically, recording the residue of the signal modulo the flux quantum in 2^p ths of a flux quantum for a p-level binary tree. Signal quantization is accomplished by comparators that read the 2^p-1 circulating currents in the leaf-level branches, providing a total of 2^p possibilities in the periodic code. The phase tree can therefore be used as a vernier, linear over a large number of periods because a single analog element determines the quantization levels once the network is properly biased. A system consisting of a conventional m-bit analog-to-digital converter (ADC m≈4-7) and an auxiliary p-bit phase tree interpolator (p≈2-5) can achieve at least m+p -1 bits without loss of bandwidth or sample rate     

Scaling `ballistic' heterojunction bipolar transistors

Reducing length scales in npn heterojunction bipolar transistors leads to unexpected changes in the fundamental limits of device performance. Very high p-type carrier concentrations in the base result in a reduced inelastic electron scattering rate. In addition, there exists a maximum base/collector bias above which ballistic collector transport is not possible, and correct scaling requires the n-type collector contact to be unusually heavily doped     

Error detection in a class of decimal codes

Consideration is given to the problem of multiple parity checks for an n-digit number. Each check relates to specific digits, where the probability p of a particular digit being in error is fixed. The author proves that it is best, in the sense of minimizing the probability of an undetected error, to add either one or n parity checks, depending on the value of n and p