Multiprocessor Out-of-Core FFTs with Distributed Memory and Parallel Disks

This paper extends an earlier out-of-core Fast Fourier Transform (FFT) method for a uniprocessor with the Parallel Disk Model (PDM) to use multiple processors. Four out-of-core multiprocessor methods are examined. Operationally, these methods differ in the size of mini-butterfly computed in memory and how the data are organized on the disks and in the distributed memory of the multiprocessor. The methods also perform differing amounts of I/O and communication. Two of them have the remarkable property that even though they are computing the FFT on a multiprocessor, all interprocessor communication occurs outside the mini-butterfly computations. Performance results on a small workstation cluster indicate that except for unusual combinations of problem size and memory size, the methods that do not perform interprocessor communication during the mini-butterfly computations require approximately 86% of the time of those that do. Moreover, the faster methods are much easier to implement

Viterbi algorithm on a hypercube: Concurrent formulation

The similarity between the Fast Fourier Transform and the Viterbi algorithm is exploited to develop a Concurrent Viterbi Algorithm suitable for a multiprocessor system interconnected as a hypercube. The proposed algorithm can efficiently decode large constraint length convolutional codes, using different degrees of parallelism, and is attractive for VLSI implementation

Ordered fast fourier transforms on a massively parallel hypercube multiprocessor

Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine

On the impact of communication complexity in the design of parallel numerical algorithms

This paper describes two models of the cost of data movement in parallel numerical algorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In the second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm independent upper bounds on system performance are derived for several problems that are important to scientific computation

Real-Time Vocal Tract Modelling

To date, most speech synthesis techniques have relied upon the representation of the vocal tract by some form of filter, a typical example being linear predictive coding (LPC). This paper describes the development of a physiologically realistic model of the vocal tract using the well-established technique of transmission line modelling (TLM). This technique is based on the principle of wave scattering at transmission line segment boundaries and may be used in one, two, or three dimensions. This work uses this technique to model the vocal tract using a one-dimensional transmission line. A six-port scattering node is applied in the region separating the pharyngeal, oral, and the nasal parts of the vocal tract