High-Speed Area-Efficient Hardware Architecture for the Efficient Detection of Faults in a Bit-Parallel Multiplier Utilizing the Polynomial Basis of GF(2m)

The utilization of finite field multipliers is pervasive in contemporary digital systems, with hardware implementation for bit parallel operation often necessitating millions of logic gates. However, various digital design issues, whether natural or stemming from soft errors, can result in gate malfunction, ultimately leading to erroneous multiplier outputs. Thus, to prevent susceptibility to error, it is imperative to employ an effective finite field multiplier implementation that boasts a robust fault detection capability. This study proposes a novel fault detection scheme for a recent bit-parallel polynomial basis multiplier over GF(2m), intended to achieve optimal fault detection performance for finite field multipliers while simultaneously maintaining a low-complexity implementation, a favored attribute in resource-constrained applications like smart cards. The primary concept behind the proposed approach is centered on the implementation of a BCH decoder that utilizes re-encoding technique and FIBM algorithm in its first and second sub-modules, respectively. This approach serves to address hardware complexity concerns while also making use of Berlekamp-Rumsey-Solomon (BRS) algorithm and Chien search method in the third sub-module of the decoder to effectively locate errors with minimal delay. The results of our synthesis indicate that our proposed error detection and correction architecture for a 45-bit multiplier with 5-bit errors achieves a 37% and 49% reduction in critical path delay compared to existing designs. Furthermore, the hardware complexity associated with a 45-bit multiplicand that contains 5 errors is confined to a mere 80%, which is significantly lower than the most exceptional BCH-based fault recognition methodologies, including TMR, Hamming's single error correction, and LDPC-based procedures within the realm of finite field multiplication.Comment: 9 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2209.1338

Criticality Aware Soft Error Mitigation in the Configuration Memory of SRAM based FPGA

Efficient low complexity error correcting code(ECC) is considered as an effective technique for mitigation of multi-bit upset (MBU) in the configuration memory(CM)of static random access memory (SRAM) based Field Programmable Gate Array (FPGA) devices. Traditional multi-bit ECCs have large overhead and complex decoding circuit to correct adjacent multibit error. In this work, we propose a simple multi-bit ECC which uses Secure Hash Algorithm for error detection and parity based two dimensional Erasure Product Code for error correction. Present error mitigation techniques perform error correction in the CM without considering the criticality or the execution period of the tasks allocated in different portion of CM. In most of the cases, error correction is not done in the right instant, which sometimes either suspends normal system operation or wastes hardware resources for less critical tasks. In this paper,we advocate for a dynamic priority-based hardware scheduling algorithm which chooses the tasks for error correction based on their area, execution period and criticality. The proposed method has been validated in terms of overhead due to redundant bits, error correction time and system reliabilityComment: 6 pages, 8 figures, conferenc

Efficient Decoder for Optical Transport Networks Achieving Near Capacity Performance

Today’s optical transport networks (OTNs) support a plethora of services such as video streaming, cloud computing, social networking and many more. To make such a wide assortment of services possible, a tremendous amount of data needs to be carried over the internet backbone supported by these optical transport networks. In order to cope with this increase in traffic, data rate on OTNs has increased significantly. Product codes (PC) are a class of codes that provide good coding gain at reasonable decoding complexity and, hence, have been a popular choice for OTNs in recent times. The key goal of this thesis is to implement a decoder for a Product Code (PC) on a Virtex7 Field Programmable Gate Array(FPGA). The product code of choice for this project is based on a (1023,993) BCH code as a component code. The conventional decoder for BCH codes has a computationally expensive step for finding the roots of error locator polynomial. The BCH decoder implemented as a part of this project is optimized to speed up the decoding process while at the same time also simplifying the hardware complexity of the design. The implementation is parallelized and pipelined to achieve high throughputs. This provides a hardware platform to evaluate the performance of product codes at low bit error rates that is infeasible using software simulations

Book Review

A Scholarly Review of “Error Control for Network-On-Chip Links” (Authors: Bo Fu and Paul Ampadu, 2012)Fu, B.; and Ampadu, P. 2012. Error Control for Network-On-Chip Links.Springer Science+Business Media, LLC, New York, NY, USA.Available: <http://dx.doi.org/10.1007/978-1-4419-9313-7>

Variable-Rate VLSI Architecture for 400-Gb/s Hard-Decision Product Decoder

Variable-rate transceivers, which adapt to the conditions, will be central to energy-efficient communication. However, fiber-optic communication systems with high bit-rate requirements make design of flexible transceivers challenging, since additional circuits needed to orchestrate the flexibility will increase area and degrade speed. We propose a variable-rate VLSI architecture of a forward error correction (FEC) decoder based on hard-decision product codes. Variable shortening of component codes provides a mechanism by which code rate can be varied, the number of iterations offers a knob to control the coding gain, while a key-equation solver module that can swap between error-locator polynomial coefficients provides a means to change error correction capability. Our evaluations based on 28-nm netlists show that a variable-rate decoder implementation can offer a net coding gain (NCG) range of 9.96-10.38 dB at a post-FEC bit-error rate of 10^-15. The decoder achieves throughputs in excess of 400 Gb/s, latencies below 53 ns, and energy efficiencies of 1.14 pJ/bit or less. While the area of the variable-rate decoder is 31% larger than a decoder with a fixed rate, the power dissipation is a mere 5% higher. The variable error correction capability feature increases the NCG range further, to above 10.5 dB, but at a significant area cost

Novel fault tolerant Multi-Bit Upset (MBU) Error-Detection and Correction (EDAC) architecture

Desde el punto de vista de seguridad, la certificación aeronáutica de aplicaciones críticas de vuelo requiere diferentes técnicas que son usadas para prevenir fallos en los equipos electrónicos. Los fallos de tipo hardware debido a la radiación solar que existe a las alturas standard de vuelo, como SEU (Single Event Upset) y MCU (Multiple Bit Upset), provocan un cambio de estado de los bits que soportan la información almacenada en memoria. Estos fallos se producen, por ejemplo, en la memoria de configuración de una FPGA, que es donde se definen todas las funcionalidades. Las técnicas de protección requieren normalmente de redundancias que incrementan el coste, número de componentes, tamaño de la memoria y peso. En la fase de desarrollo de aplicaciones críticas de vuelo, generalmente se utilizan una serie de estándares o recomendaciones de diseño como ABD100, RTCA DO-160, IEC62395, etc, y diferentes técnicas de protección para evitar fallos del tipo SEU o MCU. Estas técnicas están basadas en procesos tecnológicos específicos como memorias robustas, codificaciones para detección y corrección de errores (EDAC), redundancias software, redundancia modular triple (TMR) o soluciones a nivel sistema. Esta tesis está enfocada a minimizar e incluso suprimir los efectos de los SEUs y MCUs que particularmente ocurren en la electrónica de avión como consecuencia de la exposición a radiación de partículas no cargadas (como son los neutrones) que se encuentra potenciada a las típicas alturas de vuelo. La criticidad en vuelo que tienen determinados sistemas obligan a que dichos sistemas sean tolerantes a fallos, es decir, que garanticen un correcto funcionamiento aún cuando se produzca un fallo en ellos. Es por ello que soluciones como las presentadas en esta tesis tienen interés en el sector industrial. La Tesis incluye una descripción inicial de la física de la radiación incidente sobre aeronaves, y el análisis de sus efectos en los componentes electrónicos aeronaúticos basados en semiconductor, que desembocan en la generación de SEUs y MCUs. Este análisis permite dimensionar adecuadamente y optimizar los procedimientos de corrección que se propongan posteriormente. La Tesis propone un sistema de corrección de fallos SEUs y MCUs que permita cumplir la condición de Sistema Tolerante a Fallos, a la vez que minimiza los niveles de redundancia y de complejidad de los códigos de corrección. El nivel de redundancia es minimizado con la introducción del concepto propuesto HSB (Hardwired Seed Bits), en la que se reduce la información esencial a unos pocos bits semilla, neutros frente a radiación. Los códigos de corrección requeridos se reducen a la corrección de un único error, gracias al uso del concepto de Distancia Virtual entre Bits, a partir del cual será posible corregir múltiples errores simultáneos (MCUs) a partir de códigos simples de corrección. Un ejemplo de aplicación de la Tesis es la implementación de una Protección Tolerante a Fallos sobre la memoria SRAM de una FPGA. Esto significa que queda protegida no sólo la información contenida en la memoria sino que también queda auto-protegida la función de protección misma almacenada en la propia SRAM. De esta forma, el sistema es capaz de auto-regenerarse ante un SEU o incluso un MCU, independientemente de la zona de la SRAM sobre la que impacte la radiación. Adicionalmente, esto se consigue con códigos simples tales como corrección por bit de paridad y Hamming, minimizando la dedicación de recursos de computación hacia tareas de supervisión del sistema.For airborne safety critical applications certification, different techniques are implemented to prevent failures in electronic equipments. The HW failures at flying heights of aircrafts related to solar radiation such as SEU (Single-Event-Upset) and MCU (Multiple Bit Upset), causes bits alterations that corrupt the information at memories. These HW failures cause errors, for example, in the Configuration-Code of an FPGA that defines the functionalities. The protection techniques require classically redundant functionalities that increases the cost, components, memory space and weight. During the development phase for airborne safety critical applications, different aerospace standards are generally recommended as ABD100, RTCA-DO160, IEC62395, etc, and different techniques are classically used to avoid failures such as SEU or MCU. These techniques are based on specific technology processes, Hardened memories, error detection and correction codes (EDAC), SW redundancy, Triple Modular Redundancy (TMR) or System level solutions. This Thesis is focussed to minimize, and even to remove, the effects of SEUs and MCUs, that particularly occurs in the airborne electronics as a consequence of its exposition to solar radiation of non-charged particles (for example the neutrons). These non-charged particles are even powered at flying altitudes due to aircraft volume. The safety categorization of different equipments/functionalities requires a design based on fault-tolerant approach that means, the system will continue its normal operation even if a failure occurs. The solution proposed in this Thesis is relevant for the industrial sector because of its Fault-tolerant capability. Thesis includes an initial description for the physics of the solar radiation that affects into aircrafts, and also the analyses of their effects into the airborne electronics based on semiconductor components that create the SEUs and MCUs. This detailed analysis allows the correct sizing and also the optimization of the procedures used to correct the errors. This Thesis proposes a system that corrects the SEUs and MCUs allowing the fulfilment of the Fault-Tolerant requirement, reducing the redundancy resources and also the complexity of the correction codes. The redundancy resources are minimized thanks to the introduction of the concept of HSB (Hardwired Seed Bits), in which the essential information is reduced to a few seed bits, neutral to radiation. The correction codes required are reduced to the correction of one error thanks to the use of the concept of interleaving distance between adjacent bits, this allows the simultaneous multiple error correction with simple single error correcting codes. An example of the application of this Thesis is the implementation of the Fault-tolerant architecture of an SRAM-based FPGA. That means that the information saved in the memory is protected but also the correction functionality is auto protected as well, also saved into SRAM memory. In this way, the system is able to self-regenerate the information lost in case of SEUs or MCUs. This is independent of the SRAM area affected by the radiation. Furthermore, this performance is achieved by means simple error correcting codes, as parity bits or Hamming, that minimize the use of computational resources to this supervision tasks for system.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Luis Alfonso Entrena Arrontes.- Secretario: Pedro Reviriego Vasallo.- Vocal: Mª Luisa López Vallej