E.L. Zapata

Area-efficient architecture for Fast Fourier transform

We present an area-efficient parallel architecture that implements the constant-geometry, in-place Fast Fourier transform. It consists of a specific purpose processor array interconnected by means of a perfect unshuffle network. For a radix r transform of N=r/sup n/ data of size D and a column of P=r/sup p/ processors, each processor has only one local memory of N/rP words of size rD, with only one read port and one write port that, nevertheless, make it possible to read the r inputs of a butterfly and write r intermediate results in each memory cycle. The address generating circuit that permits the in-place implementation is simple and the same for all the local memories. The data how has been designed to efficiently exploit the pipelining of the processing section with no cycle loss. This architecture reduces the area by almost 50% of other designs with a similar performance.

CORDIC architectures with parallel compensation of the scale factor

The compensation of scale factor imposes significant computation overhead on the CORDIC algorithm. In this paper we will propose two algorithms and architectures in order to perform the compensation of the scale factor in parallel with the computation of the CORDIC iterations. This way it is not necessary to carry out the final multiplication or add scaling iterations in order to achieve the compensation. With the architectures we propose the dependence on n of the compensation of the scale factor disappears, and this considerably reduces the latency of the system. The architectures developed are optimized solutions for the different operating modes of the CORDIC both in conventional and in redundant arithmetic.

Parallel squared error clustering on hypercube arrays

Though new parallel algorithms are continually appearing in the literature, it is still quite rare for them to be capable of dealing with problems of sizes that do not conveniently fit the machine for which they are designed. This article presents the algorithm PSEC, a parallel squared error clustering algorithm for hypercube SIMD computers of arbitrary cube dimension with local memory. PSEC owes its flexibility to the association of each of the three dimensions of the problem (numbers of data points, features, and clusters) with a distinct subset of the dimensions of the hypercube.

Digit on-line large radix CORDIC rotator

Many applications figure the evaluation of rotations at high speeds. However there is a trade-off between the chip area and the latency. In this paper we develop a digit on-line pipelined array architecture based on the radix-4 CORDIC algorithm in rotation mode. The radix-4 CORDIC algorithm halves the number of microrotations with respect the traditionally radix-2 algorithm with the drawback of a non-constant scale factor. Seeking a good compromise between silicon area and latency we have used digit on-line processing. This way the data inputs the processor in blocks of bits (digits) in MSD-first mode of processing. We have used redundant carry-save arithmetic to allow carry-free additions and on-line processing. The designed processor demonstrates to have a better performance than previous digit on-line architectures.

Modified Gram-Schmidt QR factorization on hypercube SIMD computers

Abstract QR factorization is a popular calculation method in matrix algebra due to its usefulness in the solution of problems such as estimating least squares and calculating eigenvalues. In this paper, we describe a parallel algorithm for the calculation of the QR factorization on a hypercube architecture of the SIMD type with distributed memory. We have chosen the modified Gram-Schmidt method with pivoting to determine the QR factorization as it is characterized by good numerical stability. As an application of the QR factorization, we analyze the problem of least squares, developing a complementary parallel algorithm for solving it. Both algorithms are general; they are not limited by the size of the problem or the dimension of the hypercube. Finally, we analyze the algorithmic complexities of both parallel algorithms.

Parallel fuzzy clustering on fixed size hypercube SIMD computers

Abstract This article presents PFCM, a parallel algorithm for fuzzy clustering of large data sets. Being a generalization of FCM, the algorithm enables arbitrary numbers of data points, features and clusters to be handled cost-optimally by hypercube SIMD computers of arbitrary cube dimension, the only limitation being the size of the local memories of the processors. Speedup responds optimally to enlarging the hypercube. PFCM owes its flexibility to the technique employed in its derivation from the sequential fuzzy C-means algorithm FCM: the association of each of the three dimensions of the problem (numbers of data points, features and clusters) with a distinct subset of hypercube dimensions.

Image template matching on hypercube SIMD computers

Abstract We present in this work a parallel algorithm to perform an image template matching (PITM) on SIMD hypercube computers with non-shared local memory. This parallel algorithm is general in the sense that it allows for arbitrary dimensions for the image, the template and the hypercube. The flexibility of the PITM algorithm is rooted in the partition of the dimensions of the hypercube into four subsets, each one associated with one independent loop of the sequential algorithm (template matching in the domain of the time), and in the way the data are distributed in the local memories of the processing elements (consecutive storage for the template and for the matrix of cross-correlation coefficients, and shifted-consecutive for the image). Both the algorithmic complexity and the data redundancy are analyzed.

Architecture for wavelet packet transform with best tree searching

Wavelet Packet Transform (WPT) provides good spectral and temporal resolutions in arbitrary regions of the time-frequency plane. Given an additive cost function, a best-tree searching algorithm allows the selection of the best basis for a given signal according to this function. This adaptive choice of the time-frequency tiling benefits most of the applications where the standard Wavelet Transform (WT) has already shown to be useful. Though many specific architectures have been proposed in the literature for the WT, it is not the case for WPT. In this work we present a specific architecture for WPT which implements the best-tree searching algorithm.

A parallel markovian model reliability algorithm for hypercube networks

Abstract Resolution of markovian models to evaluate reliability of multiprocessor systems is a operation which requires a great amount of computations when the number of nodes is high. Therefore, this kind of models are suitable for parallel procesing. In this work we present a parallel algorithm to evaluate the reliability of multiprocessor systems with degradable nodes on SIMD hypercube computers. This parallel algorithm is general in the sense that it do not impose any restriction in the problem space dimenssions (nodes, spare, degradations and time) and is adaptable to any hypercube dimension. The flexibility of the algorithm is rooted in the methodology 3evelopped by Zapata et al. [1] for embedding algorithms into hypercubes. Finally, the algorithmic complexity is analyzed.

Detection, classification and 3D reconstruction of biological macromolecules on hypercube computers.

In this work we present results of the mapping on hypercube computers of some of the key steps involved in the procedure for 3D structural determination from transmission electron microscopy images. The goal is the introduction of parallel processing tools in the field of electron microscopy image processing. We show how the rich topology of the hypercube, combined with an efficient programming strategy, allows for order-of-magnitude increase in computational capacity for such time-consuming tasks as calculation of multidimensional FFTs, cross-correlation coefficients, fuzzy partitioning functionals and the filtered back-projection 3D reconstruction method.