P.V. Ananda Mohan

Residue Number Systems

Algorithms and Architectures

• Broschiertes Buch

Produktbeschreibung

This text is an excellent reference for both professional and academic researchers in the field of VLSI using residue number systems. It is also of interest to those working in the general fields of VLSI design, DSP design, and cryptography.

Topics covered include choice of moduli; architectures for conversion from binary to RNS; RNS to binary conversion techniques; quadratic RNS; and applications. Numerous examples illustrate the ideas developed. The area and computational requirements are highlighted for all designs, so the selection of a particular architecture is facilitated. Some of the topics covered have application in cryptography. The book includes a comprehensive bibliography in this area.

Residue Number Systems: Algorithms and Architectures is also suitable for a graduate-level course as part of a VLSI curriculum.

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There has been continuing interest in the improvement of the speed of Digital Signal processing. The use of Residue Number Systems for the design of DSP systems has been extensively researched in literature. Szabo and Tanaka have popularized this approach through their book published in 1967. Subsequently, Jenkins and Leon have rekindled the interest of researchers in this area in 1978, from which time there have been several efforts to use RNS in practical system implementation. An IEEE Press book has been published in 1986 which was a collection of Papers. It is very interesting to note that in the recent past since 1988, the research activity has received a new thrust with emphasis on VLSI design using non ROM based designs as well as ROM based designs as evidenced by the increased publications in this area. The main advantage in using RNS is that several small word-length Processors are used to perform operations such as addition, multiplication and accumulation, subtraction,thus needing less instruction execution time than that needed in conventional 16 bitl32 bit DSPs. However, the disadvantages of RNS have b. een the difficulty of detection of overflow, sign detection, comparison of two numbers, scaling, and division by arbitrary number, RNS to Binary conversion and Binary to RNS conversion. These operations, unfortunately, are computationally intensive and are time consuming.

Produktdetails

• The Springer International Series in Engineering and Computer Science 677
• Verlag: Springer / Springer US / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4613-5343-0
• Softcover reprint of the original 1st ed. 2002
• Seitenzahl: 272
• Erscheinungstermin: 31. Oktober 2012
• Englisch
• Abmessung: 235mm x 155mm x 15mm
• Gewicht: 421g
• ISBN-13: 9781461353430
• ISBN-10: 1461353432
• Artikelnr.: 39159338

Inhaltsangabe

1 Introduction.- 1.1 Historical survey.- 1.2 Basic definitions of RNS.- 1.3 Addition operation in RNS.- 1.4 Conclusion.- 2 Forward and Reverse Converters for General Moduli Set.- 2.1 Introduction.- 2.2 Mixed Radix Conversion based techniques.- 2.3 CRT based conversion techniques.- 2.4 Binary to RNS conversion techniques.- 2.5 Conclusion.- 3 Forward and Reverse Converters for General Moduli Set {2k-l,2k,2k+l}.- 3.1 Introduction.- 3.2 Forward conversion architectures.- 3.3 Reverse converters for the moduli set {2k-1, 2k, 2k+1}.- 3.4 Forward and Reverse converters for the moduli set{2k, 2k-l, 2k-1-l}.- 3.5 Forward and reverse converters for the moduli sets {2n+l, 2n,2n-l}.- 3.6 Conclusion.- 4 Multipliers for RNS.- 4.1 Introduction.- 4.2 Multipliers based on index calculus.- 4.3 Quarter square multipliers.- 4.4 Taylor's multipliers.- 4.5 Multipliers with in-built scaling.- 4.6 Razavi and Battelini architectures using periodic properties of residues.- 4.7 Hiasat's Modulo multipliers.- 4.8 Eueithy and Bayoumi modulo multiplication technique.- 4.9 Brickell's algorithm based multipliers and extensions.- 4.10 Stouraitis et al architectures for (A.X + B) mod mi realization.- 4.11 Multiplication using Redundant Number system.- 4.12 Conclusion.- 5 Base Extension, Scaling and Division Techniques.- 5.1 Introduction.- 5.2 Base extension and scaling techniques.- 5.3 Division in residue number systems.- 5.4 Scaling in the Moduli set {2n-1, 2n, 2n+1}.- 5.5 Conclusion.- 6 Error Detection and Correction in RNS.- 6.1 Introduction.- 6.2 Szabo and Tanaka technique for Error detection and Correction.- 6.3 Mendelbaum's Error correction technique.- 6.4 Jenkins's Error correction techniques.- 6.5 Ramachandran's Error correction technique.- 6.6 Su and Lo unified technique for scaling and error correction.- 6.7 Orto et al technique for error correction and detection using only one redundant modulus.- 6.8 Conclusion.- 7 Quadratic Residue Number Systems.- 7.1 Introduction.- 7.2 Basic operations in QRNS.- 7.3 Modified quadratic residue number systems.- 7.4 Jenkins and Krogmeier implementations.- 7.5 Taylor's single modulus ALU for QRNS.- 7.6 Conclusion.- 8 Applications of Residue Number Systems.- 8.1 Introduction.- 8.2 Digital Analog Converters.- 8.3 FIR Filters.- 8.4 Recursive RNS filter implementation.- 8.5 Digital frequency synthesis using RNS.- 8.6 Multiple Valued Logic Based RNS designs.- 8.7 Paliouras and Stouraitis architectures using moduli of the form rn.- 8.8 Taheri, Jullien and Miller technique of High-speed computation in rings using systolic Architectures.- 8.9 RNS based implementation of FFT structures.- 8.10 Optimum Symmetric Residue Number System.- 8.11 Conclusion.- 9 References.

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Introduction.- Modulo Addition/Subtraction.- Binary to Residue Conversion.- Modulo Multiplication.- Residue to Binary Conversion.- Scaling, Base Extension, MAgnitude Comparison, and Sign Detection.- Applications.- RNS in Cryptography.