{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T23:29:57Z","timestamp":1768519797747,"version":"3.49.0"},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2018,4,30]],"date-time":"2018-04-30T00:00:00Z","timestamp":1525046400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["CCF-1318091"],"award-info":[{"award-number":["CCF-1318091"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. Emerg. Technol. Comput. Syst."],"published-print":{"date-parts":[[2018,4,30]]},"abstract":"<jats:p>\n            Stochastic circuits (SCs) offer considerable area- and power-consumption benefits in various applications at the expense of computational inaccuracies. Unlike conventional logic synthesis, managing accuracy is a central problem in SC design. It is usually tackled in ad hoc fashion by multiple trial-and-error simulations that vary relevant parameters like the stochastic number length\n            <jats:italic>n<\/jats:italic>\n            . We present, for the first time, a systematic design approach to controlling the accuracy of SCs and balancing it against other design parameters. We express the (in)accuracy of a circuit processing\n            <jats:italic>n<\/jats:italic>\n            -bit stochastic numbers by the numerical deviation of the computed value from the expected result, in conjunction with a confidence level. Using the theory of Monte Carlo simulation, we derive expressions for the stochastic number length required for a desired level of accuracy or vice versa. We discuss the integration of the theory into a design framework that is applicable to both combinational and sequential SCs. We show that for combinational SCs, accuracy is independent of the circuit\u2019s size or complexity, a surprising result. We also show how the analysis can identify subtle errors in both combinational and sequential designs. Finally, we apply the proposed methods to a case study on filtering noisy EKG signals.\n          <\/jats:p>","DOI":"10.1145\/3183345","type":"journal-article","created":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T11:58:04Z","timestamp":1532606284000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Framework for Quantifying and Managing Accuracy in Stochastic Circuit Design"],"prefix":"10.1145","volume":"14","author":[{"given":"Florian","family":"Neugebauer","sequence":"first","affiliation":[{"name":"University of Passau, Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilia","family":"Polian","sequence":"additional","affiliation":[{"name":"University of Passau, Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John P.","family":"Hayes","sequence":"additional","affiliation":[{"name":"University of Michigan, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,7,25]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Physionet. 2017. 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Springer Science 8 Business Media."},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS\u201913)","author":"Chen Jienan","year":"2013","unstructured":"Jienan Chen and Jianhao Hu . 2013 . A novel FIR filter based on stochastic logic . In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS\u201913) . IEEE, 2050--2053. Jienan Chen and Jianhao Hu. 2013. A novel FIR filter based on stochastic logic. In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS\u201913). IEEE, 2050--2053."},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the 32nd IEEE International Conference on Computer Design (ICCD\u201914)","author":"Chen Te-Hsuan","unstructured":"Te-Hsuan Chen and John P. Hayes . 2014. Analyzing and controlling accuracy in stochastic circuits . In Proceedings of the 32nd IEEE International Conference on Computer Design (ICCD\u201914) . IEEE, 367--373. Te-Hsuan Chen and John P. Hayes. 2014. Analyzing and controlling accuracy in stochastic circuits. In Proceedings of the 32nd IEEE International Conference on Computer Design (ICCD\u201914). IEEE, 367--373."},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of the IEEE Computer Society Annual Symposium on Very Large Scale Integration Systems (ISVLSI\u201916)","author":"Chen Te-Hsuan","unstructured":"Te-Hsuan Chen and John P. Hayes . 2016. Design of division circuits for stochastic computing . In Proceedings of the IEEE Computer Society Annual Symposium on Very Large Scale Integration Systems (ISVLSI\u201916) . IEEE, 116--121. Te-Hsuan Chen and John P. Hayes. 2016. Design of division circuits for stochastic computing. In Proceedings of the IEEE Computer Society Annual Symposium on Very Large Scale Integration Systems (ISVLSI\u201916). IEEE, 116--121."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-5841-9_2"},{"key":"e_1_2_1_11_1","volume-title":"Monte Carlo Methods","author":"Hammersley John Michael","unstructured":"John Michael Hammersley and David Christopher Handscomb . 1964. Monte Carlo Methods . J. Wiley , Methuen . John Michael Hammersley and David Christopher Handscomb. 1964. Monte Carlo Methods. J. Wiley, Methuen."},{"key":"e_1_2_1_12_1","volume-title":"Compact and accurate digital filters based on stochastic computing","author":"Ichihara Hideyuki","year":"2017","unstructured":"Hideyuki Ichihara , Tatsuyoshi Sugino , Syota Ishii , Tsuyoshi Iwagaki , and Tomoo Inoue . 2017. Compact and accurate digital filters based on stochastic computing . IEEE Trans. Emerg. Topics Comput . ( 2017 ). Hideyuki Ichihara, Tatsuyoshi Sugino, Syota Ishii, Tsuyoshi Iwagaki, and Tomoo Inoue. 2017. Compact and accurate digital filters based on stochastic computing. IEEE Trans. Emerg. Topics Comput. (2017)."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCD.2011.6081391"},{"key":"e_1_2_1_14_1","doi-asserted-by":"crossref","unstructured":"Thomas M\u00fcller-Gronbach Erich Novak and Klaus Ritter. 2012. Monte Carlo-Algorithmen. Springer-Verlag.  Thomas M\u00fcller-Gronbach Erich Novak and Klaus Ritter. 2012. Monte Carlo-Algorithmen. Springer-Verlag.","DOI":"10.1007\/978-3-540-89141-3"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2011.2163630"},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT\u201913)","author":"Paler Alexandru","unstructured":"Alexandru Paler , Josef Kinseher , Ilia Polian , and John P. Hayes . 2013. Approximate simulation of circuits with probabilistic behavior . In Proceedings of the IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT\u201913) . IEEE, 95--100. Alexandru Paler, Josef Kinseher, Ilia Polian, and John P. Hayes. 2013. Approximate simulation of circuits with probabilistic behavior. In Proceedings of the IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT\u201913). IEEE, 95--100."},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the IEEE International Conference on Digital Signal Processing (DSP\u201915)","author":"Parhi Megha","unstructured":"Megha Parhi , Marc D. Riedel , and Keshab K. Parhi . 2015. Effect of bit-level correlation in stochastic computing . In Proceedings of the IEEE International Conference on Digital Signal Processing (DSP\u201915) . IEEE, 463--467. Megha Parhi, Marc D. Riedel, and Keshab K. Parhi. 2015. Effect of bit-level correlation in stochastic computing. In Proceedings of the IEEE International Conference on Digital Signal Processing (DSP\u201915). 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