Hardware implementation of a pipelined turbo decoder

Turbo codes have been widely studied since they were first proposed in 1993 by Berrou, Glavieux, and Thitimajshima in "Near Shannon Limit error-correcting coding and decoding: Turbo-codes" [1]. They have the advantage of providing a low bit error rate (BER) in decoding, and outperform linear block and convolutional codes in low signal-to-noise-ratio (SNR) environments. The decoding performance of turbo codes can be very close to the Shannon Limit, about 0.7decibel (dB). It is determined by the architectures of the constituent encoders and interleaver, but is bounded in high SNRs by an error floor. Turbo codes are widely used in communications. We explore the codeword weight spectrum properties that contribute to their excellent performance. Furthermore, the decoding performance is analyzed and compared with the free distance asymptotic performance. A 16-state turbo decoder is implemented using VHSIC Hardware Description Language (VHDL) and then mapped onto a field-programmable gate array (FPGA) board. The hardware implementations are compared with the software simulations to verify the decoding correctness. A pipelined architecture is then implemented which significantly reduces the decoding latency. -- Keywords: turbo codes; decoding performance; Monte Carlo simulations; FPGA implementatio

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

On the Cryptanalysis of Public-Key Cryptography

Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the underlying arithmetic on parallel architectures. The fastest known approach to solve the discrete logarithm problem in groups of elliptic curves over finite fields is the Pollard rho method. The negation map can be used to speed up this calculation by a factor √2. It is well known that the random walks used by Pollard rho when combined with the negation map get trapped in fruitless cycles. We show that previously published approaches to deal with this problem are plagued by recurring cycles, and we propose effective alternative countermeasures. Furthermore, fast modular arithmetic is introduced which can take advantage of prime moduli of a special form using efficient "sloppy reduction." The effectiveness of these techniques is demonstrated by solving a 112-bit elliptic curve discrete logarithm problem using a cluster of PlayStation 3 game consoles: breaking a public-key standard and setting a new world record. The elliptic curve method (ECM) for integer factorization is the asymptotically fastest method to find relatively small factors of large integers. From a cryptanalytic point of view the performance of ECM gives information about secure parameter choices of some cryptographic protocols. We optimize ECM by proposing carry-free arithmetic modulo Mersenne numbers (numbers of the form 2M – 1) especially suitable for parallel architectures. Our implementation of these techniques on a cluster of PlayStation 3 game consoles set a new record by finding a 241-bit prime factor of 21181 – 1. A normal form for elliptic curves introduced by Edwards results in the fastest elliptic curve arithmetic in practice. Techniques to reduce the temporary storage and enhance the performance even further in the setting of ECM are presented. Our results enable one to run ECM efficiently on resource-constrained platforms such as graphics processing units

New VLSI design of a MAP/BCJR decoder.

Any communication channel suffers from different kinds of noises. By employing forward error correction (FEC) techniques, the reliability of the communication channel can be increased. One of the emerging FEC methods is turbo coding (iterative coding), which employs soft input soft output (SISO) decoding algorithms like maximum a posteriori (MAP) algorithm in its constituent decoders. In this thesis we introduce a design with lower complexity and less than 0.1dB performance loss compare to the best performance observed in Max-Log-MAP algorithm. A parallel and pipeline design of a MAP decoder suitable for ASIC (Application Specific Integrated Circuits) is used to increase the throughput of the chip. The branch metric calculation unit is studied in detail and a new design with lower complexity is proposed. The design is also flexible to communication block sizes, which makes it ideal for variable frame length communication systems. A new even-spaced quantization technique for the proposed MAP decoder is utilized. Normalization techniques are studied and a suitable technique for the Max-Log-MAP decoder is explained. The decoder chip is synthesized and implemented in a 0.18 mum six-layer metal CMOS technology. (Abstract shortened by UMI.)Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .S23. Source: Masters Abstracts International, Volume: 43-05, page: 1783. Adviser: Majid Ahmadi. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Approximate Computing Strategies for Low-Overhead Fault Tolerance in Safety-Critical Applications

This work studies the reliability of embedded systems with approximate computing on software and hardware designs. It presents approximate computing methods and proposes approximate fault tolerance techniques applied to programmable hardware and embedded software to provide reliability at low computational costs. The objective of this thesis is the development of fault tolerance techniques based on approximate computing and proving that approximate computing can be applied to most safety-critical systems. It starts with an experimental analysis of the reliability of embedded systems used at safety-critical projects. Results show that the reliability of single-core systems, and types of errors they are sensitive to, differ from multicore processing systems. The usage of an operating system and two different parallel programming APIs are also evaluated. Fault injection experiment results show that embedded Linux has a critical impact on the system’s reliability and the types of errors to which it is most sensitive. Traditional fault tolerance techniques and parallel variants of them are evaluated for their fault-masking capability on multicore systems. The work shows that parallel fault tolerance can indeed not only improve execution time but also fault-masking. Lastly, an approximate parallel fault tolerance technique is proposed, where the system abandons faulty execution tasks. This first approximate computing approach to fault tolerance in parallel processing systems was able to improve the reliability and the fault-masking capability of the techniques, significantly reducing errors that would cause system crashes. Inspired by the conflict between the improvements provided by approximate computing and the safety-critical systems requirements, this work presents an analysis of the applicability of approximate computing techniques on critical systems. The proposed techniques are tested under simulation, emulation, and laser fault injection experiments. Results show that approximate computing algorithms do have a particular behavior, different from traditional algorithms. The approximation techniques presented and proposed in this work are also used to develop fault tolerance techniques. Results show that those new approximate fault tolerance techniques are less costly than traditional ones and able to achieve almost the same level of error masking.Este trabalho estuda a confiabilidade de sistemas embarcados com computação aproximada em software e projetos de hardware. Ele apresenta métodos de computação aproximada e técnicas aproximadas para tolerância a falhas em hardware programável e software embarcado que provêem alta confiabilidade a baixos custos computacionais. O objetivo desta tese é o desenvolvimento de técnicas de tolerância a falhas baseadas em computação aproximada e provar que este paradigma pode ser usado em sistemas críticos. O texto começa com uma análise da confiabilidade de sistemas embarcados usados em sistemas de tolerância crítica. Os resultados mostram que a resiliência de sistemas singlecore, e os tipos de erros aos quais eles são mais sensíveis, é diferente dos multi-core. O uso de sistemas operacionais também é analisado, assim como duas APIs de programação paralela. Experimentos de injeção de falhas mostram que o uso de Linux embarcado tem um forte impacto na confiabilidade do sistema. Técnicas tradicionais de tolerância a falhas e variações paralelas das mesmas são avaliadas. O trabalho mostra que técnicas de tolerância a falhas paralelas podem de fato melhorar não apenas o tempo de execução da aplicação, mas também seu mascaramento de erros. Por fim, uma técnica de tolerância a falhas paralela aproximada é proposta, onde o sistema abandona instâncias de execuções que apresentam falhas. Esta primeira experiência com computação aproximada foi capaz de melhorar a confiabilidade das técnicas previamente apresentadas, reduzindo significativamente a ocorrência de erros que provocam um crash total do sistema. Inspirado pelo conflito entre as melhorias trazidas pela computação aproximada e os requisitos dos sistemas críticos, este trabalho apresenta uma análise da aplicabilidade de computação aproximada nestes sistemas. As técnicas propostas são testadas sob experimentos de injeção de falhas por simulação, emulação e laser. Os resultados destes experimentos mostram que algoritmos aproximados possuem um comportamento particular que lhes é inerente, diferente dos tradicionais. As técnicas de aproximação apresentadas e propostas no trabalho são também utilizadas para o desenvolvimento de técnicas de tolerância a falhas aproximadas. Estas novas técnicas possuem um custo menor que as tradicionais e são capazes de atingir o mesmo nível de mascaramento de erros

Design Techniques for Energy-Quality Scalable Digital Systems

Energy efficiency is one of the key design goals in modern computing. Increasingly complex tasks are being executed in mobile devices and Internet of Things end-nodes, which are expected to operate for long time intervals, in the orders of months or years, with the limited energy budgets provided by small form-factor batteries. Fortunately, many of such tasks are error resilient, meaning that they can toler- ate some relaxation in the accuracy, precision or reliability of internal operations, without a significant impact on the overall output quality. The error resilience of an application may derive from a number of factors. The processing of analog sensor inputs measuring quantities from the physical world may not always require maximum precision, as the amount of information that can be extracted is limited by the presence of external noise. Outputs destined for human consumption may also contain small or occasional errors, thanks to the limited capabilities of our vision and hearing systems. Finally, some computational patterns commonly found in domains such as statistics, machine learning and operational research, naturally tend to reduce or eliminate errors. Energy-Quality (EQ) scalable digital systems systematically trade off the quality of computations with energy efficiency, by relaxing the precision, the accuracy, or the reliability of internal software and hardware components in exchange for energy reductions. This design paradigm is believed to offer one of the most promising solutions to the impelling need for low-energy computing. Despite these high expectations, the current state-of-the-art in EQ scalable design suffers from important shortcomings. First, the great majority of techniques proposed in literature focus only on processing hardware and software components. Nonetheless, for many real devices, processing contributes only to a small portion of the total energy consumption, which is dominated by other components (e.g. I/O, memory or data transfers). Second, in order to fulfill its promises and become diffused in commercial devices, EQ scalable design needs to achieve industrial level maturity. This involves moving from purely academic research based on high-level models and theoretical assumptions to engineered flows compatible with existing industry standards. Third, the time-varying nature of error tolerance, both among different applications and within a single task, should become more central in the proposed design methods. This involves designing “dynamic” systems in which the precision or reliability of operations (and consequently their energy consumption) can be dynamically tuned at runtime, rather than “static” solutions, in which the output quality is fixed at design-time. This thesis introduces several new EQ scalable design techniques for digital systems that take the previous observations into account. Besides processing, the proposed methods apply the principles of EQ scalable design also to interconnects and peripherals, which are often relevant contributors to the total energy in sensor nodes and mobile systems respectively. Regardless of the target component, the presented techniques pay special attention to the accurate evaluation of benefits and overheads deriving from EQ scalability, using industrial-level models, and on the integration with existing standard tools and protocols. Moreover, all the works presented in this thesis allow the dynamic reconfiguration of output quality and energy consumption. More specifically, the contribution of this thesis is divided in three parts. In a first body of work, the design of EQ scalable modules for processing hardware data paths is considered. Three design flows are presented, targeting different technologies and exploiting different ways to achieve EQ scalability, i.e. timing-induced errors and precision reduction. These works are inspired by previous approaches from the literature, namely Reduced-Precision Redundancy and Dynamic Accuracy Scaling, which are re-thought to make them compatible with standard Electronic Design Automation (EDA) tools and flows, providing solutions to overcome their main limitations. The second part of the thesis investigates the application of EQ scalable design to serial interconnects, which are the de facto standard for data exchanges between processing hardware and sensors. In this context, two novel bus encodings are proposed, called Approximate Differential Encoding and Serial-T0, that exploit the statistical characteristics of data produced by sensors to reduce the energy consumption on the bus at the cost of controlled data approximations. The two techniques achieve different results for data of different origins, but share the common features of allowing runtime reconfiguration of the allowed error and being compatible with standard serial bus protocols. Finally, the last part of the manuscript is devoted to the application of EQ scalable design principles to displays, which are often among the most energy- hungry components in mobile systems. The two proposals in this context leverage the emissive nature of Organic Light-Emitting Diode (OLED) displays to save energy by altering the displayed image, thus inducing an output quality reduction that depends on the amount of such alteration. The first technique implements an image-adaptive form of brightness scaling, whose outputs are optimized in terms of balance between power consumption and similarity with the input. The second approach achieves concurrent power reduction and image enhancement, by means of an adaptive polynomial transformation. Both solutions focus on minimizing the overheads associated with a real-time implementation of the transformations in software or hardware, so that these do not offset the savings in the display. For each of these three topics, results show that the aforementioned goal of building EQ scalable systems compatible with existing best practices and mature for being integrated in commercial devices can be effectively achieved. Moreover, they also show that very simple and similar principles can be applied to design EQ scalable versions of different system components (processing, peripherals and I/O), and to equip these components with knobs for the runtime reconfiguration of the energy versus quality tradeoff

Low-cost duplication for separable error detection in computer arithmetic

Low-cost arithmetic error detection will be necessary in the future to ensure correct and safe system operation. However, current error detection mechanisms for arithmetic either have high area and energy overheads or are complex and offer incomplete protection against errors. Full duplication is simple, strong, and separable, but often is prohibitively costly. Alternative techniques such as arithmetic error coding require lower hardware and energy overheads than full duplication, but they do so at the expense of high design effort and error coverage holes. The goal of this research is to mitigate the deficiencies of duplication and arithmetic error coding to form an error detection scheme that may be readily employed in future systems. The techniques described by this work use a general duplication technique that employs an alternate number system in the duplicate arithmetic unit. These novel dual modular redundancy organizations are referred to as low-cost duplication, and they provide compelling efficiency and coverage advantages over prior arithmetic error detection mechanisms.Electrical and Computer Engineerin

Design and implementation of a digital neural processor for detection applications

The main focus of this research is to develop a digital neural network (processor) and hardware (VLSI) implementation of the same for detection applications, for example in the distance protection of power transmission lines. Using a hardware neural processor will improve the protection system performance over software implementations in terms of speed of operation, response time for faults etc. The main aspects of this research are software design, performance analysis, hardware design and hardware implementation of the digital neural processor. The software design is carried out by developing an object oriented neural network simulator with backpropagation training using C++ language. A preliminary analysis shows that the inputs to the neural network need to be preprocessed. Two filters have been developed for this purpose, based on the analysis of the training data available. The performance analysis involves studying quantization effects (determination of precision requirements) in the network. -- The hardware design involves design of the neural network and the preprocessors. The neural processor consists of three types of processing elements (neurons): input, hidden and output neurons. The input neurons form the input layer of the processor which receive input from the preprocessors. The input layer can be configured to directly receive external input by changing the mode of operation. The output layer gives the signal to the relay for tripping the line under fault. Each neuron consists of datapath and local control unit. Datapath consists of the components for forward and backward passes of the processor and the register file. The local control unit controls the flow of data within a neuron and co-ordinates with the global control unit which controls the flow of data between layers. The neurons and the layers are pipelined for improving the throughput of the processor. The neural processor and the filters are implemented in VLSI using hardware description language (VHDL) and Synopsys / Cadence CAD tools. All the components are individually verified and tested for their functionality and implemented using 0.5 μ CMOS technology

A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD