Generalized polyphase representation and application to coding gain enhancement

Generalized polyphase representations (GPP) have been mentioned in literature in the context of several applications. In this paper, we provide a characterization for what constitutes a valid GPP. Then, we study an application of GPP, namely in improving the coding gains of transform coding systems. We also prove several properties of the GPP

The Telecommunications and Data Acquisition Report

This publication, one of a series formerly titled The Deep Space Network Progress Report, documents DSN progress in flight project support, tracking and data acquisition research and technology, network engineering, hardware and software implementation, and operations. In addition, developments in Earth-based radio technology as applied to geodynamics, astrophysics and the radio search for extraterrestrial intelligence are reported

Customisable arithmetic hardware designs

Imperial Users onl

Efficient high-precision integer multiplication on the GPU

Dieguez AP, Amor M, Doallo R, Nukada A, Matsuoka S. Efficient high precision integer multiplication on the GPU. The International Journal of High Performance Computing Applications. 2022;36(3):356-369.© The Author(s) 2022. Publisher: SAGE Publications. https://doi.org/10.1177/10943420221077964[Abstract]: The multiplication of large integers, which has many applications in computer science, is an operation that can be expressed as a polynomial multiplication followed by a carry normalization. This work develops two approaches for efficient polynomial multiplication: one approach is based on tiling the classical convolution algorithm, but taking advantage of new CUDA architectures, a novelty approach to compute the multiplication using integers without accuracy lossless; the other one is based on the Strassen algorithm, an algorithm that multiplies large polynomials using the FFT operation, but adapting the fastest FFT libraries for current GPUs and working on the complex field. Previous studies reported that the Strassen algorithm is an effective implementation for “large enough” integers on GPUs. Additionally, most previous studies do not examine the implementation of the carry normalization, but this work describes a parallel implementation for this operation. Our results show the efficiency of our approaches for short, medium, and large sizes.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been supported by the Ministry of Science and Innovation of Spain (PID2019-104184RB-I00), by the Galician Government and FEDER funds under the Consolidation Program of Competitive Reference Groups (UDC/GI-000265, ref. ED431C 2021/30), by the Consolidation Program of Competitive Research Units (ED431G2019/01), and by the FPU Program of the Ministry of Education of Spain (FPU14/02801). It is also partially supported by JST CREST [JPMJCR1303 and JPMJCR1687] and NVIDIA GPU Center of Excellence and conducted as research activities of AIST-TokyoTech Real World Big-Data Computation Open Innovation Laboratory (RWBC-OIL).Xunta de Galicia; ED431C 2021/3

Fast multiplication of multiple-precision integers

Multiple-precision multiplication algorithms are of fundamental interest for both theoretical and practical reasons. The conventional method requires 0(n2) bit operations whereas the fastest known multiplication algorithm is of order 0(n log n log log n). The price that has to be paid for the increase in speed is a much more sophisticated theory and programming code. This work presents an extensive study of the best known multiple-precision multiplication algorithms. Different algorithms are implemented in C, their performance is analyzed in detail and compared to each other. The break even points, which are essential for the selection of the fastest algorithm for a particular task, are determined for a given hardware software combination

Spectral modular arithmetic

In many areas of engineering and applied mathematics, spectral methods provide very powerful tools for solving and analyzing problems. For instance, large to extremely large sizes of numbers can efficiently be multiplied by using discrete Fourier transform and convolution property. Such computations are needed when computing π to millions of digits of precision, factoring and also big prime search projects. When it comes to the utilization of spectral techniques for modular operations in public key cryptosystems two difficulties arise; the first one is the reduction needed after the multiplication step and the second is the cryptographic sizes which are much shorter than the optimal asymptotic crossovers of spectral methods. In this dissertation, a new modular reduction technique is proposed. Moreover, modular multiplication is given based on this reduction. These methods work fully in the frequency domain with some exceptions such as the initial, final and partial transformations steps. Fortunately, the new technique addresses the reduction problem however, because of the extra complexity coming from the overhead of the forward and backward transformation computations, the second goal is not easily achieved when single operations such as modular multiplication or reduction are considered. On the contrary, if operations that need several modular multiplications with respect to the same modulus are considered, this goal is more tractable. An obvious example of such an operation is the modular exponentiation i.e., the computation of c=m[superscript e] mod n where c, m, e, n are large integers. Therefore following the spectral modular multiplication operation a new modular exponentiation method is presented. Since forward and backward transformation calculations do not need to be performed for every multiplication carried during the exponentiation, the asymptotic crossover for modular exponentiation is decreased to cryptographic sizes. The method yields an efficient and highly parallel architecture for hardware implementations of public-key cryptosystems

On the synthesis and processing of high quality audio signals by parallel computers

This work concerns the application of new computer architectures to the creation and manipulation of high-quality audio bandwidth signals. The configuration of both the hardware and software in such systems falls under consideration in the three major sections which present increasing levels of algorithmic concurrency. In the first section, the programs which are described are distributed in identical copies across an array of processing elements; these programs run autonomously, generating data independently, but with control parameters peculiar to each copy: this type of concurrency is referred to as isonomic}The central section presents a structure which distributes tasks across an arbitrary network of processors; the flow of control in such a program is quasi- indeterminate, and controlled on a demand basis by the rate of completion of the slave tasks and their irregular interaction with the master. Whilst that interaction is, in principle, deterministic, it is also data-dependent; the dynamic nature of task allocation demands that no a priori knowledge of the rate of task completion be required. This type of concurrency is called dianomic? Finally, an architecture is described which will support a very high level of algorithmic concurrency. The programs which make efficient use of such a machine are designed not by considering flow of control, but by considering flow of data. Each atomic algorithmic unit is made as simple as possible, which results in the extensive distribution of a program over very many processing elements. Programs designed by considering only the optimum data exchange routes are said to exhibit systolic^ concurrency. Often neglected in the study of system design are those provisions necessary for practical implementations. It was intended to provide users with useful application programs in fulfilment of this study; the target group is electroacoustic composers, who use digital signal processing techniques in the context of musical composition. Some of the algorithms in use in this field are highly complex, often requiring a quantity of processing for each sample which exceeds that currently available even from very powerful computers. Consequently, applications tend to operate not in 'real-time' (where the output of a system responds to its input apparently instantaneously), but by the manipulation of sounds recorded digitally on a mass storage device. The first two sections adopt existing, public-domain software, and seek to increase its speed of execution significantly by parallel techniques, with the minimum compromise of functionality and ease of use. Those chosen are the general- purpose direct synthesis program CSOUND, from M.I.T., and a stand-alone phase vocoder system from the C.D.P..(^4) In each case, the desired aim is achieved: to increase speed of execution by two orders of magnitude over the systems currently in use by composers. This requires substantial restructuring of the programs, and careful consideration of the best computer architectures on which they are to run concurrently. The third section examines the rationale behind the use of computers in music, and begins with the implementation of a sophisticated electronic musical instrument capable of a degree of expression at least equal to its acoustic counterparts. It seems that the flexible control of such an instrument demands a greater computing resource than the sound synthesis part. A machine has been constructed with the intention of enabling the 'gestural capture' of performance information in real-time; the structure of this computer, which has one hundred and sixty high-performance microprocessors running in parallel, is expounded; and the systolic programming techniques required to take advantage of such an array are illustrated in the Occam programming language