Rehan Hafiz

A low latency generic accuracy configurable adder

High performance approximate adders typically comprise of multiple smaller sub-adders, carry prediction units and error correction units. In this paper, we present a low-latency generic accuracy configurable adder to support variable approximation modes. It provides a higher number of potential configurations compared to state-of-the-art, thus enabling a high degree of design flexibility and trade-off between performance and output quality. An error correction unit is integrated to provide accurate results for cases where high accuracy is required. Furthermore, an associated scheme for error probability estimation allows convenient comparison of different approximate adder configurations without requiring the need to numerically simulate the adder. Our experimental results validate the developed error model and also the lower latency of our generic accuracy configurable adder over state-of-the-art approximate adders. For functional verification and prototyping, we have used a Xilinx Virtex-6 FPGA. Our adder model and synthesizable RTL are made open-source.

Invited - Cross-layer approximate computing: from logic to architectures

We present a survey of approximate techniques and discuss concepts for building power-/energy-efficient computing components reaching from approximate accelerators to arithmetic blocks (like adders and multipliers). We provide a systematical understanding of how to generate and explore the design space of approximate components, which enables a wide-range of power/energy, performance, area and output quality tradeoffs, and a high degree of design flexibility to facilitate their design. To enable cross-layer approximate computing, bridging the gap between the logic layer (i.e. arithmetic blocks) and the architecture layer (and even considering the software layers) is crucial. Towards this end, this paper introduces open-source libraries of low-power and high-performance approximate components. The elementary approximate arithmetic blocks (adder and multiplier) are used to develop multi-bit approximate arithmetic blocks and accelerators. An analysis of data-driven resilience and error propagation is discussed. The approximate computing components are a first steps towards a systematic approach to introduce approximate computing paradigms at all levels of abstractions.

Probabilistic Error Modeling for Approximate Adders

Approximate adders are widely being advocated as a means to achieve performance gain in error resilient applications. In this paper, a generic methodology for analytical modeling of probability of occurrence of error and the Probability Mass Function (PMF) of error value in a selected class of approximate adders is presented, which can serve as performance metrics for the comparative analysis of various adders and their configurations. The proposed model is applicable to approximate adders that comprise of sub-adder units of uniform as well as non-uniform lengths. Using a systematic methodology, we derive closed form expressions for the probability of error for a number of state-of-the-art high-performance approximate adders. The probabilistic analysis is carried out for arbitrary input distributions. It can be used to study the dependence of error statistics in an adder’s output on its configuration and input distribution. Moreover, it is shown that by building upon the proposed error model, we can estimate the probability of error in circuits with multiple approximate adders. We also demonstrate that, using the proposed analysis, the comparative performance of different approximate adders can be correctly predicted in practical applications of image processing.

An area-efficient consolidated configurable error correction for approximate hardware accelerators

Approximate adders are widely being advocated for developing hardware accelerators to perform complex arithmetic operations. Most of the state-of-the-art accuracy configurable approximate adders utilize some integrated Error Detection and Correction (EDC) circuitry. Consequently, the accumulated area overhead due to the EDC (integrated within individual adders) is significant. In this paper, we propose a low-cost Consolidated Error Correction (CEC) unit, that essentially corrects the accumulated error at the accelerator output. The proposed CEC is based on a mathematical model of approximation error. We integrate our CEC unit in approximate hardware accelerators deployed in different applications to demonstrate its area savings and speed enhancement compared to state-of-the-art.

Digitally balanced detection for optical tomography

Analog balanced Photodetection has found extensive usage for sensing of a weak absorption signal buried in laser intensity noise. This paper proposes schemes for compact, affordable, and flexible digital implementation of the already established analog balanced detection, as part of a multichannel digital tomography system. Variants of digitally balanced detection (DBD) schemes, suitable for weak signals on a largely varying background or weakly varying envelopes of high frequency carrier waves, are introduced analytically and elaborated in terms of algorithmic and hardware flow. The DBD algorithms are implemented on a low-cost general purpose reconfigurable hardware (field-programmable gate array), utilizing less than half of its resources. The performance of the DBD schemes compare favorably with their analog counterpart: A common mode rejection ratio of 50 dB was observed over a bandwidth of 300 kHz, limited mainly by the host digital hardware. The close relationship between the DBD outputs and those of known analog balancing circuits is discussed in principle and shown experimentally in the example case of propane gas detection.

Automatic selection of color reference image for panoramic stitching

Color correction is an important step in the generation of high-resolution stitched panoramas. Typically, color correction schemes try to match the color of each image in the panorama to an arbitrarily selected reference image. We provide a scheme that uses quantitative metrics such as image contrast, gradient-based structure similarity index measure (G-SSIM) and color clipping information to automatically select the best reference that results in visually pleasing output panoramas. Quantitative and qualitative evaluation of the scheme show encouraging results for panoramic images as well as for stitched videos. The scheme acts as a pre-processing step to color correction and its applicability to both parametric and non-parametric global color correction schemes has also been demonstrated.

Stabilization of panoramic videos from mobile multi-camera platforms

Wide field of view panoramic videos have recently become popular due to the availability of high resolution displays. These panoramic videos are generated by stitching video frames captured from a panoramic video acquisition system, typically comprising of multiple video cameras arranged on a static or mobile platform. A mobile panoramic video acquisition system may suffer from global mechanical vibrations as well as independent inter-camera vibrations resulting in a jittery panoramic video. While existing stabilization schemes generally tackle single-camera vibrations, they do not account for these inter-camera vibrations. In this paper, we propose a video stabilization technique for multi-camera panoramic videos under the consideration that independent jitter may be exhibited by content of each camera. The proposed method comprises of three steps; the first step removes the global jitter in the video by estimating collective motion and subsequently removing the high frequency component from it. The second step removes the independent i.e. local jitter of each camera by estimating motion of each camera content separately. Pixels that are located in the overlapping regions of panoramic video are contributed by neighboring cameras, therefore, the estimated camera motion for these pixels is weighted using the blend masks generated by the stitching process. The final step applies local geometric warping to the stitched frames and removes any residual jitter induced due to parallax. Experimental results prove that proposed scheme performs better than existing panoramic stabilization schemes. Display Omitted Stabilization of panoramic and stabilization of single camera videos are separate problems.Panoramic videos suffer from global and inter-camera vibrations.Blend-masks are useful for dealing with inter-camera vibrations.Our survey suggests that viewers prefer this scheme over prior works.

Automatic Reference Selection for Parametric Color Correction Schemes for Panoramic Video Stitching

Panoramic views enhance the immersive visual experience by providing seamless high resolution image formed by stitching multiple low resolution images or videos. Color correction is a fundamental step in this process that operates to match the color of individual views with each other. Typically, one arbitrary view is taken as a reference and colors of the remaining views are matched to the reference view. This paper presents a scheme for automated selection of a reference image that results in a high contrast, visually appealing stitched panorama. The scheme is computationally efficient and applicable to a broad range of global parametric color correction schemes.

Optical Absorption Measurements in Particle-Containing Ambients Using Gated Ratiometric Detection

We demonstrate a ldquotrading time for signalrdquo approach for the measurement of species-specific optical transmission, in ambients rich in particulates, using the example case of a turbulent fluidized bed reactor. The method is introduced on the basis of Monte Carlo simulations, as well as analysis of experimental data, of beam propagation for a range of path lengths, and particle concentrations. In a particular embodiment for relative propane-concentration measurements, data is acquired only during gated time intervals of partial beam occlusion detected in real time. The digitized data streams from the signal and background beams is processed by algorithms performing gating, digital balanced detection, and dual wavelength ratiometry. This combination, implemented on inexpensive programmable hardware, results in at least an order of magnitude improvement in sensitivity.

Probabilistic Error Analysis of Approximate Recursive Multipliers

Approximate multipliers are gaining importance in energy-efficient computing and require careful error analysis. In this paper, we present the error probability analysis for recursive approximate multipliers with approximate partial products. Since these multipliers are constructed from smaller approximate multiplier building blocks, we propose to derive the error probability in an arbitrary bit-width multiplier from the probabilistic model of the basic building block and the probability distributions of inputs. The analysis is based on common features of recursive multipliers identified by carefully studying the behavioral model of state-of-the-art designs. By building further upon the analysis, Probability Mass Function (PMF) of error is computed by individually considering all possible error cases and their inter-dependencies. We further discuss the generalizations for approximate adder trees, signed multipliers, squarers and constant multipliers. The proposed analysis is validated by applying it to several state-of-the-art approximate multipliers and comparing with corresponding simulation results. The results show that the proposed analysis serves as an effective tool for predicting, evaluating and comparing the accuracy of various multipliers. Results show that for the majority of the recursive multipliers, we get accurate error performance evaluation. We also predict the multipliers’ performance in an image processing application to demonstrate its practical significance.