arXiv subjects

P Balasubramanian

Publications and source records attributed to P Balasubramanian.

At least 19 recordsLinked to original sources

arXiv2023

Fault-Tolerant Design Approach Based on Approximate Computing

Triple Modular Redundancy (TMR) has been traditionally used to ensure complete tolerance to a single fault or a faulty processing unit, where the processing unit may be a circuit or a system. However, TMR incurs more than 200% overhead in terms of area and power compared to a single processing unit. Hence, alternative redundancy approaches were proposed in the literature to mitigate the design overheads associated with TMR, but they provide only partial or moderate fault tolerance. This research presents a new fault-tolerant design approach based on approximate computing called FAC that has the same fault tolerance as TMR and achieves significant reductions in the design metrics for physical implementation. FAC is suited for a plethora of error-tolerant applications. Here, the performance of TMR and FAC has been evaluated for a digital image processing application. The image processing results obtained confirm the usefulness of FAC. When an example processing unit was implemented using a 28-nm CMOS technology, FAC achieved a 15.3% reduction in delay, a 19.5% reduction in area, and a 24.7% reduction in power compared to TMR.

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arXiv2021

Gate-Level Static Approximate Adders

This work compares and analyzes static approximate adders which are suitable for FPGA and ASIC type implementations. We consider many static approximate adders and evaluate their performance with respect to a digital image processing application using standard figures of merit such as peak signal to noise ratio and structural similarity index metric. We provide the error metrics of approximate adders, and the design metrics of accurate and approximate adders corresponding to FPGA and ASIC type implementations. For the FPGA implementation, we considered a Xilinx Artix-7 FPGA, and for an ASIC type implementation, we considered a 32-28 nm CMOS standard digital cell library. While the inferences from this work could serve as a useful reference to determine an optimum static approximate adder for a practical application, in particular, we found approximate adders HOAANED, HERLOA and M-HERLOA to be preferable.

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arXiv2020

Area Optimized Quasi Delay Insensitive Majority Voter for TMR Applications

Mission-critical and safety-critical applications generally tend to incorporate triple modular redundancy (TMR) to embed fault tolerance in their physical implementations. In a TMR realization, an original function block, which may be a circuit or a system, and two exact copies of the function block are used to successfully overcome any temporary fault or permanent failure of an arbitrary function block during the routine operation. The corresponding outputs of the function blocks are majority voted using 3-input majority voters whose outputs define the outputs of a TMR realization. Hence, a 3-input majority voter forms an important component of a TMR realization. Many synchronous majority voters and an asynchronous non-delay insensitive majority voter have been presented in the literature. Recently, quasi delay insensitive (QDI) asynchronous majority voters for TMR applications were also discussed in the literature. In this regard, this paper presents a new QDI asynchronous majority voter for TMR applications, which is better optimized in area compared to the existing QDI majority voters. The proposed QDI majority voter requires 30.2% less area compared to the best of the existing QDI majority voters, and this could be useful for resource-constrained fault tolerance applications. The example QDI TMR circuits were implemented using a 32/28nm complementary metal oxide semiconductor (CMOS) process. The delay insensitive dual rail code was used for data encoding, and 4-phase return-to-zero and return-to-one handshake protocols were used for data communication.

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arXiv2019

Performance Comparison of Quasi-Delay-Insensitive Asynchronous Adders

In this technical note, we provide a comparison of the design metrics of various quasi-delay-insensitive (QDI) asynchronous adders, where the adders correspond to diverse architectures. QDI adders are robust, and the objective of this technical note is to point to those QDI adders which are suitable for low power/energy and less area. This information could be valuable for a resource-constrained low power VLSI design scenario. Non-QDI adders are excluded from the comparison since they are not robust although they may have optimized design metrics. All the QDI adders were realized using a 32/28nm CMOS process.

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arXiv2019

Indicating Asynchronous Multipliers

Multiplication is a basic arithmetic operation that is encountered in almost all general-purpose microprocessing and digital signal processing applications, and multiplication is physically realized using a multiplier. This paper discusses the physical implementation of indicating asynchronous multipliers, which are inherently elastic and are robust to timing, process, and parametric variations, and are modular. We consider the physical implementation of many weak-indication asynchronous multipliers using a 32/28-nm CMOS technology by adopting the array multiplier architecture. The multipliers are synthesized in a semi-custom ASIC-design style. The 4-phase return-to-zero (RTZ) and the 4-phase return-to-one (RTO) handshake protocols are considered for the data communication. The multipliers are realized using strong-indication or weak-indication full adders. Strong-indication 2-input AND function is used to generate the partial products in the case of both RTZ and RTO handshaking. The full adders considered are derived from different indicating asynchronous logic design methods. Among the multipliers considered, a weak-indication asynchronous multiplier utilizing the biased weak-indication full adder is found to be efficient in terms of the cycle time and the power-cycle time product with respect to both RTZ and RTO handshaking. Also, the 4-phase RTO handshake protocol is found to be preferable than the 4-phase RTZ handshake protocol for achieving enhanced optimizations in the design metrics.

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arXiv2019

Indicating Asynchronous Array Multipliers

Multiplication is an important arithmetic operation that is frequently encountered in microprocessing and digital signal processing applications, and multiplication is physically realized using a multiplier. This paper discusses the physical implementation of many indicating asynchronous array multipliers, which are inherently elastic and modular and are robust to timing, process and parametric variations. We consider the physical realization of many indicating asynchronous array multipliers using a 32/28nm CMOS technology. The weak-indication array multipliers comprise strong-indication or weak-indication full adders, and strong-indication 2-input AND functions to realize the partial products. The multipliers were synthesized in a semi-custom ASIC design style using standard library cells including a custom-designed 2-input C-element. 4x4 and 8x8 multiplication operations were considered for the physical implementations. The 4-phase return-to-zero (RTZ) and the 4-phase return-to-one (RTO) handshake protocols were utilized for data communication, and the delay-insensitive dual-rail code was used for data encoding. Among several weak-indication array multipliers, a weak-indication array multiplier utilizing a biased weak-indication full adder and the strong-indication 2-input AND function is found to have reduced cycle time and power-cycle time product with respect to RTZ and RTO handshaking for 4x4 and 8x8 multiplications. Further, the 4-phase RTO handshaking is found to be preferable to the 4-phase RTZ handshaking for achieving enhanced optimizations of the design metrics.

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arXiv2019

Asynchronous Early Output Block Carry Lookahead Adder with Improved Quality of Results

A new asynchronous early output block carry lookahead adder (BCLA) incorporating redundant carries is proposed. Compared to the best of existing semi-custom asynchronous carry lookahead adders (CLAs) employing delay-insensitive data encoding and following a 4-phase handshaking, the proposed BCLA with redundant carries achieves 13% reduction in forward latency and 14.8% reduction in cycle time compared to the best of the existing CLAs featuring redundant carries with no area or power penalty. A hybrid variant involving a ripple carry adder (RCA) in the least significant stages i.e. BCLA-RCA is also considered that achieves a further 4% reduction in the forward latency and a 2.4% reduction in the cycle time compared to the proposed BCLA featuring redundant carries without area or power penalties.

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arXiv2019

Majority and Minority Voted Redundancy for Safety-Critical Applications

A new majority and minority voted redundancy (MMR) scheme is proposed that can provide the same degree of fault tolerance as N-modular redundancy (NMR) but with fewer function units and a less sophisticated voting logic. Example NMR and MMR circuits were implemented using a 32/28nm CMOS process and compared. The results show that MMR circuits dissipate less power, occupy less area, and encounter less critical path delay than the corresponding NMR circuits while providing the same degree of fault tolerance. Hence the MMR is a promising alternative to the NMR to efficiently implement high levels of redundancy in safety-critical applications.

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arXiv2018

Performance Comparison of some Synchronous Adders

This technical note compares the performance of some synchronous adders which correspond to the following architectures: i) ripple carry adder (RCA), ii) recursive carry lookahead adder (RCLA), iii) hybrid RCLA-RCA with the RCA used in the least significant adder bit positions, iv) block carry lookahead adder (BCLA), v) hybrid BCLA-RCA with the RCA used in the least significant adder bit positions, and vi) non-uniform input partitioned carry select adders (CSLAs) without and with the binary to excess-1 code (BEC) converter. The 32-bit addition was considered as an example operation. The adder architectures mentioned were implemented by targeting a typical case PVT specification (high threshold voltage, supply voltage of 1.05V and operating temperature of 25 degrees Celsius) of the Synopsys 32/28nm CMOS technology. The comparison leads to the following observations: i) the hybrid CCLA-RCA is preferable to the other adders in terms of the speed, the power-delay product, and the energy-delay product, ii) the non-uniform input partitioned CSLA without the BEC converter is preferable to the other adders in terms of the area-delay product, and iii) the RCA incorporating the full adder present in the standard digital cell library is preferable to the other adders in terms of the power-delay-area product.

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arXiv2018

Critique of "Asynchronous Logic Implementation Based on Factorized DIMS"

This paper comments on "Asynchronous Logic Implementation Based on Factorized DIMS" [Journal of Circuits, Systems, and Computers, vol. 26, no. 5, 1750087: 1-9, May 2017] with respect to two main problematic issues: i) the gate orphan problem implicit in the factorized DIMS approach discussed in the referenced article which affects its strong-indication, and ii) how the enumeration of product terms to represent the synthesis cost is skewed in the referenced article because the logic expression contains sum of products and also product of sums. It is observed that the referenced article has not provided a general logic synthesis algorithm excepting only an example illustration involving a 3-input AND logic function. The absence of a general logic synthesis algorithm would make it difficult to reproduce the research described in the referenced article. Moreover, the example illustration in the referenced article describes an unsafe logic decomposition which is not suitable for the multi-level synthesis of strong-indication asynchronous circuits. Further, a logic synthesis method which safely decomposes the DIMS solution to synthesize multi-level strong-indication asynchronous circuits is available in the existing literature, which was neither cited nor taken up for comparison in the referenced article, which is another drawback. Subsequently, it is concluded that the referenced article has not advanced existing knowledge in the field but on the contrary, has caused confusions. Hence, in the interest of readers, this paper additionally highlights some important and relevant literature which provide valuable information about robust asynchronous circuit synthesis techniques which employ delay-insensitive codes for data representation and processing and the 4-phase return-to-zero handshake protocol for data communication.

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arXiv2018

Asynchronous Ripple Carry Adder based on Area Optimized Early Output Dual-Bit Full Adder

This technical note presents the design of a new area optimized asynchronous early output dual-bit full adder (DBFA). An asynchronous ripple carry adder (RCA) is constructed based on the new asynchronous DBFAs and existing asynchronous early output single-bit full adders (SBFAs). The asynchronous DBFAs and SBFAs incorporate redundant logic and are encoded using the delay-insensitive dual-rail code (i.e. homogeneous data encoding) and follow a 4-phase return-to-zero handshaking. Compared to the previous asynchronous RCAs involving DBFAs and SBFAs, which are based on homogeneous or heterogeneous delay-insensitive data encodings and which correspond to different timing models, the early output asynchronous RCA incorporating the proposed DBFAs and/or SBFAs is found to result in reduced area for the dual-operand addition operation and feature significantly less latency than the asynchronous RCAs which consist of only SBFAs. The proposed asynchronous DBFA requires 28.6% less silicon than the previously reported asynchronous DBFA. For a 32-bit asynchronous RCA, utilizing 2 stages of SBFAs in the least significant positions and 15 stages of DBFAs in the more significant positions leads to optimization in the latency. The new early output 32-bit asynchronous RCA containing DBFAs and SBFAs reports the following optimizations in design metrics over its counterparts: i) 18.8% reduction in area than a previously reported 32-bit early output asynchronous RCA which also has 15 stages of DBFAs and 2 stages of SBFAs, ii) 29.4% reduction in latency than a 32-bit early output asynchronous RCA containing only SBFAs.

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arXiv2018

Comments on "Dual-rail asynchronous logic multi-level implementation"

In this research communication, we comment on "Dual-rail asynchronous logic multi-level implementation" [Integration, the VLSI Journal 47 (2014) 148-159] by expounding the problematic issues, and provide some clarifications on delay-insensitivity, robust asynchronous logic, multi-level decomposition, and physical implementation.

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arXiv2018

Approximate Early Output Asynchronous Adders Based on Dual-Rail Data Encoding and 4-Phase Return-to-Zero and Return-to-One Handshaking

Approximate computing is emerging as an alternative to accurate computing due to its potential for realizing digital circuits and systems with low power dissipation, less critical path delay, and less area occupancy for an acceptable trade-off in the accuracy of results. In the domain of computer arithmetic, several approximate adders and multipliers have been designed and their potential have been showcased versus accurate adders and multipliers for practical digital signal processing applications. Nevertheless, in the existing literature, almost all the approximate adders and multipliers reported correspond to the synchronous design method. In this work, we consider robust asynchronous i.e. quasi-delay-insensitive realizations of approximate adders by employing delay-insensitive codes for data representation and processing, and the 4-phase handshake protocols for data communication. The 4-phase handshake protocols used are the return-to-zero and the return-to-one protocols. Specifically, we consider the implementations of 32-bit approximate adders based on the return-to-zero and return-to-one handshake protocols by adopting the delay-insensitive dual-rail code for data encoding. We consider a range of approximations varying from 4-bits to 20-bits for the least significant positions of the accurate 32-bit asynchronous adder. The asynchronous adders correspond to early output (i.e. early reset) type, which are based on the well-known ripple carry adder architecture. The experimental results show that approximate asynchronous adders achieve reductions in the design metrics such as latency, cycle time, average power dissipation, and silicon area compared to the accurate asynchronous adders. Further, the reductions in the design metrics are greater for the return-to-one protocol compared to the return-to-zero protocol. The design metrics were estimated using a 32/28nm CMOS technology.

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arXiv2017

An Asynchronous Early Output Full Adder and a Relative-Timed Ripple Carry Adder

This article presents the design of a new asynchronous early output full adder which when cascaded leads to a relative-timed ripple carry adder (RCA). The relative-timed RCA requires imposing a very small relative-timing assumption to overcome the problem of gate orphans associated with internal carry propagation. The relative-timing assumption is however independent of the RCA size. The primary benefits of the relative-timed RCA are processing of valid data incurs data-dependent forward latency, while the processing of spacer involves a very fast constant time reverse latency of just 1 full adder delay which represents the ultimate in the design of an asynchronous RCA with the fastest reset. The secondary benefits of the relative-timed RCA are it achieves good optimization of power and area metrics simultaneously. A 32-bit relative-timed RCA constructed using the proposed early output full adder achieves respective reductions in forward latency by 67%, 10% and 3.5% compared to the optimized strong-indication, weak-indication, and early output 32-bit asynchronous RCAs existing in the literature. Based on a similar comparison, the proposed 32-bit relative-timed RCA achieves corresponding reductions in cycle time by 83%, 12.7% and 6.4%. In terms of area, the proposed 32-bit relative-timed RCA occupies 27% less Silicon than its optimized strong-indication counterpart and 17% less Silicon than its optimized weak-indication counterpart, and features increased area occupancy by a meager 1% compared to the optimized early output 32-bit asynchronous RCA. The average power dissipation of all the asynchronous 32-bit RCAs are found to be comparable since they all satisfy the monotonic cover constraint. The simulation results obtained correspond to a 32/28nm CMOS process.

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arXiv2017

A Fault Tolerance Improved Majority Voter for TMR System Architectures

For digital system designs, triple modular redundancy (TMR), which is a 3-tuple version of N-modular redundancy is widely preferred for many mission-control and safety-critical applications. The TMR scheme involves two-times duplication of the simplex system hardware, with a majority voter ensuring correctness provided at least two out of three copies of the system remain operational. Thus the majority voter plays a pivotal role in ensuring the correct operation of the system. The fundamental assumption implicit in the TMR scheme is that the majority voter does not become faulty, which may not hold well for implementations based on latest technology nodes with dimensions of the order of just tens of nanometers. To overcome the drawbacks of the classical majority voter some new voter designs were put forward in the literature with the aim of enhancing the fault tolerance. However, these voter designs generally ensure the correct system operation in the presence of either a faulty function module or the faulty voter, considered only in isolation. Since multiple faults may no longer be excluded in the nanoelectronics regime, simultaneous fault occurrences on both the function module and the voter should be considered, and the fault tolerance of the voters have to be analyzed under such a scenario. In this context, this article proposes a new fault-tolerant majority voter which is found to be more robust to faults than the existing voters in the presence of faults occurring internally and/or externally to the voter. Moreover, the proposed voter features less power dissipation, delay, and area metrics based on the simulation results obtained by using a 32/28nm CMOS process.

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arXiv2017

Design of Synchronous Section-Carry Based Carry Lookahead Adders with Improved Figure of Merit

The section-carry based carry lookahead adder (SCBCLA) architecture was proposed as an efficient alternative to the conventional carry lookahead adder (CCLA) architecture for the physical implementation of computer arithmetic. In previous related works, self-timed SCBCLA architectures and synchronous SCBCLA architectures were realized using standard cells and FPGAs. In this work, we deal with improved realizations of synchronous SCBCLA architectures designed in a semi-custom fashion using standard cells. The improvement is quantified in terms of a figure of merit (FOM), where the FOM is defined as the inverse product of power, delay and area. Since power, delay and area of digital designs are desirable to be minimized, the FOM is desirable to be maximized. Starting from an efficient conventional carry lookahead generator, we show how an optimized section-carry based carry lookahead generator is realized. In comparison with our recent work dealing with standard cells based implementation of SCBCLAs to perform 32-bit addition of two binary operands, we show in this work that with improved section-carry based carry lookahead generators, the resulting SCBCLAs exhibit significant improvements in FOM. Compared to the earlier optimized hybrid SCBCLA, the proposed optimized hybrid SCBCLA improves the FOM by 88.3%. Even the optimized hybrid CCLA features improvement in FOM by 77.3% over the earlier optimized hybrid CCLA. However, the proposed optimized hybrid SCBCLA is still the winner and has a better FOM than the currently optimized hybrid CCLA by 15.3%. All the CCLAs and SCBCLAs are implemented to realize 32-bit dual-operand binary addition using a 32/28nm CMOS process.

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arXiv2017

System Reliability, Fault Tolerance and Design Metrics Tradeoffs in the Distributed Minority and Majority Voting Based Redundancy Scheme

The distributed minority and majority voting based redundancy (DMMR) scheme was recently proposed as an efficient alternative to the conventional N-modular redundancy (NMR) scheme for the physical design of mission/safety-critical circuits and systems. The DMMR scheme enables significant improvements in fault tolerance and design metrics compared to the NMR scheme albeit at the expense of a slight decrease in the system reliability. In this context, this paper studies the system reliability, fault tolerance and design metrics tradeoffs in the DMMR scheme compared to the NMR scheme when the majority logic group of the DMMR scheme is increased in size relative to the minority logic group. Some example DMMR and NMR systems were realized using a 32/28nm CMOS process and compared. The results show that 5-of-M DMMR systems have a similar or better fault tolerance whilst requiring similar or fewer function modules than their counterpart NMR systems and simultaneously achieve optimizations in design metrics. Nevertheless, 3-of-M DMMR systems have the upper hand with respect to fault tolerance and design metrics optimizations than the comparable NMR and 5-of-M DMMR systems. With regard to system reliability, NMR systems are closely followed by 5-of-M DMMR systems which are closely followed by 3-of-M DMMR systems. The verdict is 3-of-M DMMR systems are preferable to implement higher levels of redundancy from a combined system reliability, fault tolerance and design metrics perspective to realize mission/safety-critical circuits and systems.

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arXiv2017

Asynchronous Early Output Section-Carry Based Carry Lookahead Adder with Alias Carry Logic

A new asynchronous early output section-carry based carry lookahead adder (SCBCLA) with alias carry output logic is presented in this paper. To evaluate the proposed SCBCLA with alias carry logic and to make a comparison with other CLAs, a 32-bit addition operation is considered. Compared to the weak-indication SCBCLA with alias logic, the proposed early output SCBCLA with alias logic reports a 13% reduction in area without any increases in latency and power dissipation. On the other hand, in comparison with the early output recursive CLA (RCLA), the proposed early output SCBCLA with alias logic reports a 16% reduction in latency while occupying almost the same area and dissipating almost the same average power. All the asynchronous CLAs are quasi-delay-insensitive designs which incorporate the delay-insensitive dual-rail data encoding and adhere to the 4-phase return-to-zero handshaking. The adders were realized and the simulations were performed based on a 32/28nm CMOS process.

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