Digital signal processing application based on residue number system

Tato práce se zabývá systémem zbytkových tříd a jeho aplikacemi v digitálních obvodech. První část se zabývá VHDL návrhem různých typů sčítaček v systému zbytkových tříd a jejich porovnání se standartními sčítačkami. V druhé části je implementován obrázkový processor který pracuje v systému zbytkových tříd a jeho výkonostní analýza. V textu je popsán postup návrhu a jsou prezentovány výsledky analýz.This work deals with residue number system and its applications in digital circuits. The first part is VHDL design of different adder types in residue number system and their comparison with regular adders. The second part is VHDL implementation of image processor that computes in residue number system and its performance analysis. Presented text contains description of design procedures and presentation of analysis results.

Integrated photonics modular arithmetic processor

Integrated photonics computing has emerged as a promising approach to overcome the limitations of electronic processors in the post-Moore era, capitalizing on the superiority of photonic systems. However, present integrated photonics computing systems face challenges in achieving high-precision calculations, consequently limiting their potential applications, and their heavy reliance on analog-to-digital (AD) and digital-to-analog (DA) conversion interfaces undermines their performance. Here we propose an innovative photonic computing architecture featuring scalable calculation precision and a novel photonic conversion interface. By leveraging Residue Number System (RNS) theory, the high-precision calculation is decomposed into multiple low-precision modular arithmetic operations executed through optical phase manipulation. Those operations directly interact with the digital system via our proposed optical digital-to-phase converter (ODPC) and phase-to-digital converter (OPDC). Through experimental demonstrations, we showcase a calculation precision of 9 bits and verify the feasibility of the ODPC/OPDC photonic interface. This approach paves the path towards liberating photonic computing from the constraints imposed by limited precision and AD/DA converters.Comment: 23 pages, 9 figure

Application of Residue Arithmetic in Communication and Signal Processing

Residue Number System (RNS) is a non-weighted number system. In RNS, the arithmetic operations are split into smaller parallel operations which are independent of each other. There is no carry propagation between these operations. Hence devices operating in this principle inherit property of high speed and low power consumption. But this property makes overflow detection is very difficult. Hence the moduli set is chosen such that there is no carry generated. In this thesis, the use of residue number system (RNS) is portrayed in designing solution to various applications of Communication and Signal Processing. RNS finds its application where integer arithmetic is authoritative process, since residue arithmetic operates efficiently on integers. New moduli set selection process, magnitude comparison routine and sign detection methods were limed on the onset of this dissertation. A good example of integer arithmetic is digital image. The pixels are represented by 8 bit unsigned number. Thus the operations are primarily unsigned and restricted to a small range. Hereby, in this thesis, a novel image encryption technique is depicted. The results show the robustness and timeliness of this technique. This technique is further compared to some of industry standard encryption algorithms for analysis based on robustness, encryption time and various other paradigms. Filters are signal conditioners. Each filter functions by accepting an input signal, blocking pre-specified frequency components, and passing the original signal minus those components to the output. A lowpass filter allows only low frequency signals (below some specified cutoff) through to its output, so it can be used to eliminate high frequencies. A novel design approach for a low pass filter based on residue arithmetic was also proposed. Some trite techniques as well as novel approaches were adopted to solve the design challenges. A technique for mapping the data in another space providing the liberty to work with floating numbers with a precision was adopted. PN sequence generator based on residue arithmetic is also formulated. This algorithm generates a pseudo-noise sequence which further was used to evince a spread spectrum multiuser communication system. The results are compared with trite techniques like Gold and Kasami sequence generators

Redundant residue number system code for fault-tolerant hybrid memories

Hybrid memories are envisioned as one of the alternatives to existing semiconductor memories. Although offering enormous data storage capacity, low power consumption, and reduced fabrication complexity (at least for the memory cell array), such memories are subject to a high degree of intermittent and transient faults leading to reliability issues. This article examines the use of Conventional Redundant Residue Number System (C-RRNS) error correction code, which has been extensively used in digital signal processing and communication, to detect and correct intermittent and transient cluster faults in hybrid memories. It introduces a modified version of C-RRNS, referred to as 6M-RRNS, to realize the aims at lower area overhead and performance penalty. The experimental results show that 6M-RRNS realizes a competitive error correction capability, provides larger data storage capacity, and offers higher decoding performance as compared to C-RRNS and Reed-Solomon (RS) codes. For instance, for 64-bit hybrid memories at 10% fault rate, 6M-RRNS has 98.95% error correction capability, which is 0.35% better than RS and 0.40% less than C-RRNS. Moreover, when considering 1Tbit memory, 6M-RRNS offers 4.35% more data storage capacity than RS and 11.41% more than C-RRNS. Additionally, it decodes up to 5.25 times faster than C-RRNS

Fault-tolerant computation using algebraic homomorphisms

Also issued as Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1992.Includes bibliographical references (p. 193-196).Supported by the Defense Advanced Research Projects Agency, monitored by the U.S. Navy Office of Naval Research. N00014-89-J-1489 Supported by the Charles S. Draper Laboratories. DL-H-418472Paul E. Beckmann

Number Systems for Deep Neural Network Architectures: A Survey

Deep neural networks (DNNs) have become an enabling component for a myriad of artificial intelligence applications. DNNs have shown sometimes superior performance, even compared to humans, in cases such as self-driving, health applications, etc. Because of their computational complexity, deploying DNNs in resource-constrained devices still faces many challenges related to computing complexity, energy efficiency, latency, and cost. To this end, several research directions are being pursued by both academia and industry to accelerate and efficiently implement DNNs. One important direction is determining the appropriate data representation for the massive amount of data involved in DNN processing. Using conventional number systems has been found to be sub-optimal for DNNs. Alternatively, a great body of research focuses on exploring suitable number systems. This article aims to provide a comprehensive survey and discussion about alternative number systems for more efficient representations of DNN data. Various number systems (conventional/unconventional) exploited for DNNs are discussed. The impact of these number systems on the performance and hardware design of DNNs is considered. In addition, this paper highlights the challenges associated with each number system and various solutions that are proposed for addressing them. The reader will be able to understand the importance of an efficient number system for DNN, learn about the widely used number systems for DNN, understand the trade-offs between various number systems, and consider various design aspects that affect the impact of number systems on DNN performance. In addition, the recent trends and related research opportunities will be highlightedComment: 28 page

RNS-aritmetiikka DSP-järjestelmissä

Digitaalisella signaalinkäsittelyllä (Digital Signal Processing, DSP) tarkoitetaan kaikenlaista äänen, kuvan ja muiden signaalien käsittelyä. Suosituimmat sovellukset signaalinkäsittelyssä ovat suodattimet ja Fourier-muunnokset. Signaalinkäsittelyllä tarkoitetaan monesti myös diskreettiä Fourier-muunnosta (Discrete Fourier Transform, DFT) ja tarkemmin sen jatkomuunnosta, nopeaa Fourier-muunnosta (Fast Fourier Transform, FFT). DSP-tekniikat ovat viimeaikoina olleet suuressa tutkimuskohteen suosiossa ja sen ansiosta ne ovat kehittyneet huomattavaa tahtia tällä vuosituhannella. Tärkeimpänä signaalinkäsittelyn osa-alueena on ollut alusta lähtien FFT. Tämän avulla muunnos on mahdollista tehdä paljon nopeammin ja tehokkaammin kuin normaalilla DFT-muunnoksella. Residue-numerojärjestelmän (Residue Number System, RNS) aritmetiikalla pystytään vielä lisäämään nopeutta ja tehokkuutta entisestään. RNS on numerojärjestelmä kuten tavallinen luonnollinen kymmenkanta, tai kuten digitaalisissa järjestelmissä binääriluku. Tosin se eroaa edellisistä huomattavasti, sillä RNS-luvuilla ei ole kiinteää kantaa vaan se on numeromanipulaatio. RNS koostuu moduuleista, joilla jokaisella on oma painotus. RNS-järjestelmän suurimmat hyödyt ovat nopeudessa, rinnakkaisuudessa ja virheenkestossa. Järjestelmän rinnakkaisuus tuo esiin suurimmat hyödyt sillä jokainen moduuli voidaan laskea samanaikaisesti. Tämä näkyy suoraan nopeudessa ja yleisesti tehokkuudessa. RNS-järjestelmällä on kuitenkin suuria rajoituksia ja ongelmakohtia. Nämä ovat selvästi rajoittaneet sen suosiota ja kunnollista läpilyöntiä erilaisissa digitaalisissa sovelluksissa. Jotta RNS-järjestelmää on soveliasta käyttää, on sen suunnitteluun siis panostettava paljon. Tietyt moduulivariaatiot ovat yleisesti tulleet suosituksi ja näin ollen näitä on eniten käytetty sekä tutkittu. RNS-järjestelmän käyttöä on rajoittanut myös paljon sen käännökset binääriluvusta RNS-luvuksi ja takaisin. Varsinkin takaisinkäännös binääriluvuksi on ollut koko RNS-järjestelmän suurin haaste alusta asti, mikä on jarruttanut sen suurempaa suosiota

High speed convolution using residue number systems

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1989.Title as it appears in the M.I.T. Graduate List, Feb. 1989: Number theoretic methods in digital signal processing.Includes bibliographical references (leaves 124-126).by Kurt Anthony Locher.M.S