ABSTRACT Distributed deep neural networks (DDNNs) have emerged as a promising solution to enhance the efficiency of deep learning tasks compared to traditional centralized cloud‐based Deep Neural Networks (DNNs) by distributing the computational workload across cloud, fog, and edge nodes. Although model parameter changes caused by the well‐known soft error effects have shown considerable degradation in the performance and reliability of DNNs, the resiliency of DDNNs against these effects is still understudied. This paper conducts a comprehensive analysis of the error resiliency of DDNNs, focusing on the impact of soft errors at various network layers. Using Docker containers to emulate real‐world scenarios, the study evaluates SqueezeNet and MobileNetV2 models trained on CIFAR‐100 and CIFAR‐10 datasets under varying bit error rates (BER). The obtained results demonstrate that up to a certain BER, errors introduce uncertainty in the edge node of DDNNs while beyond this BER threshold, the edge node becomes significantly compromised due to faults, leading to a high likelihood of false decisions. Increasing uncertainty causes the decision‐making process to shift to the fog and cloud nodes, leading to a considerable increase in response time. The insights from this study not only deepen our understanding of fault tolerance in DDNNs but also lay the groundwork for creating more resilient and efficient distributed learning architectures. By utilizing Docker‐based emulation, our approach provides a flexible and reproducible experimental framework that can be adapted for further studies in this area. Additionally, the findings highlight the need for adaptive strategies that can intelligently manage errors and computational resources across cloud, fog, and edge layers. These results are particularly relevant for time‐sensitive applications like autonomous vehicles, industrial IoT systems, and smart city infrastructures, where the reliability and speed of DDNNs are critical.

The most advanced ASIC-based approximate adders are focused on gate or transistor level approximating structures. However, due to architectural differences between ASIC and FPGA, comparable performance gains for FPGA-based approximate adders cannot be obtained using ASIC-based approximation ones. In this paper, we propose a method for designing a low-error approximate adder that effectively deploys the modern FPGA structure. We introduce an FPGA-based approximate adder, named as Majority Approximate Adder (MAA), with less error than the advanced approximate adders. MAA is constructed using an approximate part and an accurate one; i.e. the accurate part is based on a smaller carry-chain compared with the carry-chain of the corresponding accurate adder. In addition, approximate part is designed to use FPGA resources efficiently with a low mean error distance (MED). Experimental results based on Monte-Carlo simulation demonstrates that a 16-bit MAA has a 49.92% lower MED than the state of the art FPGA-based approximate adder. MAA also takes up less area and consumes less power than other FPGA-based approximate adders in the literature.

With the CMOS technology scaling, transistor aging has become one major issue affecting circuit reliability and lifetime. There are two major classes of existing studies that model the aging effects in the circuit delay. One is at transistor-level, which is highly accurate but very slow. The other is at gate-level, which is faster but less accurate. Moreover, most prior studies only consider a limited subset or limited value ranges of aging factors.

Traditionally, increasing logical masking probability has been used to improve the circuit reliability against single-event transients (SETs). As the very first work, this paper presents a new approach to increase the reliability of digital circuits against soft errors caused by multiple event transients (METs) by taking advantages of circuit partitioning and local logical restructuring techniques. In the proposed approach, the circuit is partitioned into various subcircuits and, then, several structures of each subcircuits which satisfy the area constraints are extracted by using a graph-based procedure. In order to select the suitable alternative between various subcircuit structures, we introduce a novel metric named global failure probability in the presence of METs (GFPM). This parameter provides an evaluation of each subcircuits contribution in the soft error rate (SER) of the given circuit making it possible to estimate the impacts of changing the structure of the subcircuits on the circuit SER. Hence, it prevents from repeatedly calculating the SER of the circuit that is very time-consuming leading to significant improvements in the optimization runtime. Experimental studies on ISCAS benchmark circuits show that the proposed approach, on average, achieves 18.4% SER reduction with 11.9% area overhead and 8.2% delay overhead comparing to the original circuit while the global SET-based SER mitigation approach and the global MET-based SER mitigation approach achieve 8.46% and 21.8% SER reduction, respectively. Besides, the proposed technique is about $580 \times $ faster than the global MET-based method.

Current technology scaling trends aggressively increases the susceptibility of combinational circuit reliability to radiation-induced transient faults (which also known as soft errors). Various gate sizing techniques have been used to reduce soft error rate (SER) in the past, but their main drawback is that they are expensive in term of run time. These methods require changes to adapt to the large scale circuits. In this paper, an efficient circuit partitioning-based gate sizing method is presented, which significantly speeds up the gate sizing optimization process. In the proposed method, the circuit is divided into the topologically levelized small subcircuits by cone structures. Then, the subcircuits which are located in the same level are resized individually and independently. The subcircuit error probability (SEP) metric is introduced to evaluate the contribution of each subcircuit into the total circuit SER. The key idea of the proposed method is to evaluate the effects of each gate sizing on circuit reliability locally using SEP instead of global evaluation by the total circuit SER. Such evaluation results in speeding up the gate sizing optimization process. Experimental results show that the proposed approach is about 280× orders of magnitude faster than the sensitivity-based gate sizing approach [R. R. Rao, D. Blaauw, and D. Sylvester, “Soft error reduction in combinational logic using gate resizing and flipflop selection,” in Proc. IEEE/ACM Int. Conf. Comput.-Aided Des., 2006, pp. 502-509] while it can achieve up to 45% reduction in circuit SER with less than 17% area overhead. This level of speed and efficiency makes the proposed approach a viable solution to mitigate the SER of very large combinational circuits used in industry.

Soft errors in combinational logic circuits are emerging as a significant reliability concern for nanoscale VLSI designs. This paper presents a novel sensitivity-based gate sizing methodology to reduce the soft error rate (SER) of combinational circuits in the presence of process variations. The proposed method is based on modeling the statistics of SER of the circuit gates as a random variable to formulate a statistical optimization problem. A backward traversing algorithm with capability for incremental analysis is developed for computing the distribution of circuit gates of SER random variables. We present a gate resizing algorithm in which the gates with the most contribution to the circuit SER are selected in a candidate set using a statistical ordering approach. The proposed algorithm trades off SER reduction and area overheads. The experimental results show that using the proposed methodology, the circuit statistical SER can be reduced by up to 56.4% compared with the 14.8% SER reduction of a circuit obtained using the worst case methodology at the expense of 10% area overhead under 10% process variation ratio. The results also show that the proposed method achieves about 40% more SER reduction compared with that obtained using closed-form analysis for statistical soft error rate estimation (CASSER), the most recently published similar work, in the same experimental conditions. Comparing the runtime of the proposed optimization algorithm with the optimization based on CASSER, it is observed that the proposed method is two orders of magnitude faster than CASSER due to its incremental analysis property.

This paper presents a novel circuit optimization technique to reduce soft error rates (SER) of combinational logic circuits in the presence of process variations. We take advantage of gate sizing technique which has been shown to be one of the most effective methods for SER mitigation in digital circuits. A statistical SER (SSER) estimation approach is proposed to be used to prune the circuit graph into a smaller set of candidate gates. Then, we perform incremental statistical sensitivity computations to determine the resizing step that are the largest improvement to circuit SER. The proposed algorithm trades off SER reduction and area overhead. Experimental results on a variety of benchmarks show SER reductions of 67.3% with gate sizing approach, with 5.5% area overheads and delay improvement of 3.2%, on average. The runtimes for the optimization algorithms are on the order of 10 minutes.

Soft error rate (SER) estimation is becoming more and more important since nanometer digital integrated circuits are getting increasingly vulnerable to soft errors. In this paper, a novel approach is proposed for soft error rate analysis of digital combinational circuit considering all masking factors. We introduce a concept called Probabilistic Vulnerability Window (PVW) which is an inference of the necessary conditions for a Single Event Transient (SET) to cause observable errors in the circuit. A computation model is proposed to calculate PVW's for all circuit gate outputs. Using the computation model, the proposed method estimates the soft error rate of the circuit by computing the probabilistic vulnerability windows in a backward approach. Experimental results show that the proposed method increases the SER computation speed by 1000X, with less than 10% accuracy loss when compared to the Monte-Carlo based fault injection methods. The results also show than the proposed approach keeps its efficiency when it is applied for estimating the soft error rate considering various SET's with different initial widths while the runtime of traditional SER estimation methods increases rapidly in such cases.

Carbon Nanotube Field Effect Transistors (CNFETs) show great promise as extensions to silicon CMOS. However, CNFET-based circuits will face great fabrication challenges that will translate into important parameter variations and decreased reliability. Hence, asynchronous logic, which is intrinsically more robust to variability, seems an ideal and perhaps unavoidable choice for digital circuits in CNFET technology. This article presents the results on the design and analysis of a CNFET-based implementation of an asynchronous circuit primitive: the Muller C-element. Using a CNFET SPICE model, we evaluate the robustness of CNFET-based C-element in the presence of CNT fabrication-related nonidealities. We investigate a quantitative evaluation of how timing variability impacts the functionality of a C-element and then, extract the necessary delay constraints of the C-element circuit from the signal transition graph specification. Considering the large degrees of spatial correlation observed between the CNFETs fabricated on directionally grown CNTs, a layout technique is exploited to overcome the robustness challenges of a CNFET-based C-element. Extensive Monte Carlo simulations on the proposed technique have demonstrated the effectiveness of the proposed CNFET-based C-element by improving approximately 50X in its robustness in expense of 65% area, 47% delay, and 56% power consumption overheads. Experimental results indicate that implementation of some CNFET-based Quasi Delay Insensitive (QDI) benchmark circuits using the proposed C-element results in significant robustness improvement with negligible power and throughput overheads. As a promising step toward CNFET-based giga-scale integrated circuits, this article shows that the asynchronous logic is an effective approach to design robust integrated circuits in CNFET technology with inherent extreme physical variations.

Carbon nanotube field effect transistors (CNFETs) show great promise as extensions to silicon CMOS. However, imperfections, which are mainly related to carbon nanotubes (CNTs) growth process, result in metallic and nonuniform CNTs leading to significant functional yield reduction. This paper presents a comprehensive technique for statistical functional yield estimation and enhancement of CNFET-based VLSI circuits. Based on experimental data extracted from aligned CNTs, we propose a compact statistical model to estimate the failure probability of a CNFET. Using the proposed failure model, we show that enhancing the CNT synthesis process alone cannot achieve acceptable functional yield for upcoming CNFET-based VLSI circuits. We propose a technique which is based on replacing each transistor by series-parallel transistor structures to reduce the failure probability of CNFETs in the presence of metallic and nonuniform CNTs. The technique is adapted to use single directional independence, which is inherent in aligned CNTs, to enhance the functional yield as validated by theoretical analysis and simulation results. Tradeoffs between failure probability reduction and design overheads such as area and current drive are explored. As demonstrated by extensive simulation results, the proposed technique achieves 80% functional yield in CNFET technology at the cost of 7.5X area and 34% current drive overheads if the CNT density and the fraction of semiconducting CNTs are improved to 200 CNTs per μm and 99.99%, respectively.