Approximate logic circuits for low overhead, non-intrusive concurrent error detection

This paper presents a procedure for synthesizing multilevel circuits with concurrent error detection based on Bose-Lin codes (1985). Bose-Lin codes are an efficient solution for providing concurrent error detection as they are separable codes and have a fixed number of check bits, independent of the number of information bits. Furthermore, Bose-Lin code checkers have a simple structure as they are based on modulo operations. Procedures are described for synthesizing circuits in a way that their structure ensures that all single-point faults can only cause errors that are detected by a Bose-Lin code. This paper also presents an efficient scheme for concurrent error detection in sequential circuits. Both the state bits and the output bits are encoded with a Bose-Lin code and their checking is combined such that one checker suffices. Results indicate low area overhead. The cost of concurrent error detection is reduced significantly compared to other methods.

Approximate circuit design is an emerging paradigm in which a designer deliberately changes the specified Boolean function to reduce area, delay, and/or power consumption of a circuit. This paper focuses on the synthesis of approximate logic circuits (or ALS) under a given error constraint. In particular, we consider ALS for a two-level design under an error rate constraint. A dynamic programming-based algorithm is proposed to find a nearly optimal approximate function by identifying the most promising set of cubes to be added to the on-set of the original function. Then, an off-the-shelf two-level logic synthesis tool is applied to further optimize the sum-of-product (SOP) expression. The experimental results show that the literal reduction is close to the optimal solution when the error rate constraint is tight and that more than 50% literal reduction is achieved for error rate below 0.8% for an 8-bit adder and a square root circuit.

This paper presents a concurrent error detection (CED) scheme for orthogonal Latin square (OLS) parallel decoders. Different from a CED scheme found in the technical literature that protects only the syndrome generator, the proposed CED scheme protects the whole OLS decoder for single stuck-at faults. This paper presents the detailed design and analysis of the proposed CED scheme and shows that it is strongly fault secured for single stuck-at faults. Extensive simulation results are also provided; different figures of merit such as area, power dissipation, gate depth, and coverage are assessed. It is shown that the proposed decoder designs for ( n, k) t-bit error correcting OLS codes (k = 16 ...256; t = 2 ...5) have reasonable overhead; for example, the average area overhead of the proposed CED is 35.5 (23.6) % compared with an OLS decoder with no CED (i.e., the previously reported CED scheme). However, the most significant advantage of the proposed scheme is that it achieves 100% fault coverage for the whole CED circuit, thus providing a very efficient and fully fault-tolerant implementation. The proposed CED is applicable to both binary and nonbinary OLS codes; the CED for a nonbinary OLS decoder achieves comparable or better results than a binary OLS decoder. Moreover, simulation shows that the proposed CED scheme is better than double modular redundancy.

Synthesis tools for approximate sequential circuits require the ability to quickly, efficiently, and automatically characterize and bound the errors produced by the circuits. Previous approaches to characterize errors in approximate sequential circuits have been based on simulations spanning all cycles of a sequential computation. These approaches, however, are not scalable and only accommodate small circuit modules and short computation times. In this paper, we observe that the statistical properties of errors in many approximate sequential circuits follow patterns that can be easily learned. Therefore, statistical error characteristics of these approximate sequential circuits can be predicted with high accuracy using only a few cycles of characterization data. Based on this novel observation, we propose a methodology for predicting error statistics in approximate sequential circuits that is accurate, fully automated, and has significantly lower overhead than prior approaches. Our methodology is robust to changes in predicted error metrics, circuit input distributions, and types of approximate hardware modules used in approximate circuits. We demonstrate the accuracy and scalability of our approach over a range of sequential circuits. On average, prediction inaccuracy is less than 2% and error characterization time is reduced by 99% compared to a simulation-based approach.

TMR is a very effective technique to mitigate SEU effects in FPGAs, but it is often expensive in terms of FPGA resource utilization and power consumption. For certain applications, Partial TMR can be used to trade off the reliability with the cost of mitigation. In this work we propose a new approach to build Partial TMR circuits for FPGAs using approximate logic circuits. This approach is scalable, with a low granularity, and can provide an optimal balance between reliability and overheads. The proposed approach has been validated using fault injection.

Many applications produce acceptable results when their underlying computations are executed in an approximate manner. For such applications, approximate circuits enable hardware implementations that exhibit improved efficiency for a given quality. Previous efforts have largely focused on the design of approximate combinational logic blocks such as adders and multipliers. In practice, however, designers are concerned with the quality of outputs generated by a sequential circuit after several cycles of computation, rather than an embedded combinational block. We propose ASLAN (Automatic methodology for Sequential Logic ApproximatioN), the first effort towards the synthesis of approximate sequential circuits. Given a sequential circuit and an output quality constraint, ASLAN creates an approximate version of the circuit that consumes lower energy, while meeting the specified quality bound. The key challenges in approximating sequential circuits are (i) to model how errors due to approximations are generated, re-circulate through the combinational logic over multiple cycles of operation, and eventually impact quality of the final output, and (ii) to select the most beneficial approximations, i.e., those that result in higher energy savings for smaller impact on quality. ASLAN addresses the first challenge by constructing a virtual Sequential Quality Constraint Circuit (SQCC) and utilizing formal verification techniques to ensure that the selected approximations meet the quality constraint. To address the second challenge, ASLAN identifies combinational blocks in the sequential circuit that are amenable to approximation, generates local quality-energy trade-off curves for them, and uses a gradient-descent approach to iteratively approximate the entire sequential circuit. We used ASLAN to automatically synthesize approximate versions of ten sequential benchmarks, resulting in energy reductions of 1.20X-2.44X for tight quality constraints, and 1.32X-4.42X for moderate quality constraints. We present case studies of using the approximate circuits generated by ASLAN in two popular applications - MPEG Encoding and K-Means Clustering - obtaining 1.32X energy savings with 0.5% PSNR degradation, and 1.26X energy savings with 0.8% increase in mean cluster radius, respectively.

Concurrent Error Detection (CED) methods are commonly employed to provide some level of error detection capability at the cost of some area and power overhead. In many applications, however, the error detection capability must be reconfigured dynamically, in order to adapt to the available power budget, criticality of the processed data, a thermal-safe schedule, etc. In this work, we propose a reconfigurable duplication-based CED infrastructure for logic circuits. The key idea is to enable/disable the operation of the duplicate circuit according to a set of control conditions. When CED is disabled, the inputs to the duplicate circuit retain their previous values (i.e., reduction in power dissipation via elimination of switching activity), yet errors are not detected (i.e., reduction in CED coverage). Experimental results using judicious and random selection of control conditions yield the same end-result; power dissipation is commensurate with CED coverage. Therefore, LFSR structures can be used to easily generate and reconfigure conditions, enabling their dynamic adjustment to adapt to the power constraints of the system.

We present a Concurrent Error Detection (CED) scheme for the Scheduler of a modern microprocessor. The proposed CED scheme is based on monitoring a set of invariances imposed through added hardware, violation of which signifies the occurrence of an error. The novelty of our solution stems from the workload-cognizant way in which these invariances are selected so that they leverage the application-level error masking inherent in program execution. Specifically, in order to ensure cost-effectiveness of the hardware employed to construct these invariances, we make use of information regarding the type and frequency of errors affecting the typical workload of the microprocessor. Thereby, we identify the most susceptible aspects of instruction execution and we accordingly distribute CED resources to protect them. Our approach is demonstrated on the Scheduler of an Alpha-like superscalar microprocessor with dynamic scheduling, hybrid branch prediction and out-of-order execution capabilities. Using an extensive fault-simulation infrastructure that we developed around this microprocessor, we profile the impact of Scheduler faults across a variety of different SPEC2000 benchmarks. Based on the results, we construct a CED scheme which monitors the time and location of instruction execution, the executed operation, the utilized resources, as well as the executed and retired sequence of instructions. At a hardware cost of only 32 percent of the Scheduler, the corresponding CED scheme detects over 85 percent of its faults that affect the architectural state of the microprocessor. Furthermore, over 99.5 percent of these faults are detected before they corrupt the architectural state, while the average detection latency for the remaining faults is in the order of a few clock cycles, implying that efficient recovery methods can be developed.

The use of deep sub-micron technology raises a number of concerns about reliability in VLSI circuits. Shrinking geometries and reduced power supplies leave the circuits vulnerable to 'soft' and transient errors. The combination of high clock speed and large circuit area result in high power consumption and skew in clock distribution. This paper investigates the use of concurrent error detection (CED) and asynchronous design to overcome these problems. Four pipelined processor designs are compared - two synchronous, two asynchronous with one of each type using CED. Initial results indicate an area overhead of 12% in return for a fault coverage of 98.54% of all unidirectional errors. Additionally, the asynchronous CED processor has an area overhead of only 4% when compared to the synchronous non-CED design.

In reversible circuits, a fault as a change in logic value at a circuit node always alters an output logic value, so observability of faults at the output is 100%. In other words, reversible circuits are latent-fault-free. Our motivation is to incorporate this unique feature of reversible circuits to design CMOS circuits having perfect or 100% Concurrent Error Detection (CED). For this purpose we propose a new, fault preservative, and reversible gate library called Even Target Mixed Polarity Multiple Control Toffoli (ET-MPMCT). By using ET-MPCT, we ensure that the parity, even or odd, is preserved at all levels including the output level unless there is a faulty node. Our design strategy has two steps for a reversible function: 1) implement the reversible functions with the ET-MPMCT library; and 2) apply reversible-to-CMOS gate conversion. In case an irreversible function needs to be synthesized then its reversible form is used followed by the two design steps. As a result, we have come up with a CMOS circuit having 100% CED. The performance of our approach is compared with other CED schemes in the literature in terms of area, detection rate, and power consumption. Simulations are done with Cadence Genus tool using TSMC $0.18 \mu \mathrm{m}$ technology. Clearly, results are in favor of our proposed technique.

Concurrent Error Detection (CED) techniques based on hardware duplication are widely used to enhance system dependability. All CED techniques contain some form of redundancy. In this paper we present simulation results to quantitatively compare various CED schemes based on their area overhead and protection (data integrity) they provide against multiple failures. We describe some studies of parity based concurrent error detection in S-boxes. In this work substitution blocks of PP-1 block-cipher, designed for platforms with very limited resources (for example for embedded systems), are used as a case study.

Fault-based side-channel cryptanalysis is a useful technique against symmetrical and asymmetrical encryption/decryption algorithms. Thus, eliminating cryptographic computation errors become critical in preventing such kind of attacks. A simple way to eliminating cryptographic computation errors is to output correct or corrected ciphers. Multiplication is the most important finite field arithmetic operation in the cryptographic computations. By using time redundancy technique, a novel dual basis (DB) multiplier over Galois fields (2m) will be presented with lower space complexity and feedback-free property. Based on the proposed feedback-free DB multiplier, the DB multiplier with a concurrent error detection (CED) capability is also easily developed. Compared with the existing DB multiplier with CED capability, the proposed one saves about 90% of time-area complexity. No existing DB multiplier in the literature has concurrent error correction (CEC) capability. Based on the proposed DB multiplier, a novel DB multiplier with CEC capability is easily designed. The proposed DB multiplier with CEC capability requires only about 3% of extra space complexity and 15% of time complexity when compared with the proposed DB multiplier without CEC.

Conventional logic synthesis systems are targeted towards reducing the area required by a logic block, as measured by the literal count or gate count; or, improving the performance in terms of gate delays; or, improving the testability of the synthesized circuit, as measured by the irredundancy of the resultant circuit. In this paper, we address the problem of developing reliability driven logic synthesis algorithms for multilevel logic circuits, which are integrated within the MIS synthesis system. Our procedures are based on concurrent error detection techniques that have been proposed in the past for two level circuits, and adapting those techniques to multilevel logic synthesis algorithms. Three schemes for concurrent error detection in a multilevel circuit are proposed in this paper, using which all the single stuck at faults in the circuit can be detected concurrently. The first scheme uses duplication of a given multilevel circuit with the addition of a totally self-checking comparator. The second scheme proposes a procedure to generate the multilevel circuit from a two level representation under some constraint such that, the Berger code of the output vector can be used to detect any single fault inside the circuit, except at the inputs. A constrained technology mapping procedure is also presented in this paper. The third scheme is based on parity codes on the outputs. The outputs are partitioned using a novel partitioning algorithm, and each partition is implemented using a multilevel circuit. Some additional parity coded outputs are generated. In all three schemes, all the necessary checkers are generated automatically and the whole circuit is placed and routed using the Timberwolf layout package. The area overheads for several benchmark examples are reported in this paper. The entire procedure is integrated into a new system called RSYN.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fault-based cryptanalysis has been developed to effectively break both private-key and public-key cryptosystems, making robust finite field multiplication a very important research topic in recent years. However, no robust normal basis multiplier has been proposed in the literature. Therefore, this investigation presents a semisystolic Gaussian normal basis multiplier. Based on the proposed Gaussian normal basis multiplier, both concurrent error detection and correction capabilities can be easily achieved using time redundancy technology with no hardware modification.

It gives importance about motion estimation (ME) as a top priority in video coding and testing. Extended BIST schemes are primarily concerned with memory circuit and testing concerns in video coding systems. Furthermore, by improving the abilities of Concurrent Error Detection, an dependability on several Processing Element will got increased. CED can discover mistakes by looking for inconsistencies and undesirable consequences from operations on the same operands. Concurrent Error Detection involves testing any route with full throttle without having to shut down the entire system. Focusing upon that Concurrent Error Detection idea, this work provides a unique Error - detecting Data Retrieval structure based here on Residue-Quotient code to identify faults &#x0026; restore information in Processing Units of Motion Estimation in video coding testing analysers.