{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T11:36:17Z","timestamp":1767008177890,"version":"3.37.3"},"reference-count":110,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012306","name":"Universit\u00e0 degli Studi di Trieste through D13-FRA-23 Line A Project","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012306","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Open J. Commun. Soc."],"published-print":{"date-parts":[[2023]]},"DOI":"10.1109\/ojcoms.2023.3332838","type":"journal-article","created":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T19:11:20Z","timestamp":1700075480000},"page":"3051-3101","source":"Crossref","is-referenced-by-count":10,"title":["Explicitly Invertible Approximations of the Gaussian Q-Function: A Survey"],"prefix":"10.1109","volume":"4","author":[{"given":"Alessandro","family":"Soranzo","sequence":"first","affiliation":[{"name":"Department of Mathematics and Geosciences, Università degli Studi di Trieste, Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4105-8084","authenticated-orcid":false,"given":"Francesca","family":"Vatta","sequence":"additional","affiliation":[{"name":"Department of Engineering and Architecture, Università degli Studi di Trieste, Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7261-1247","authenticated-orcid":false,"given":"Massimiliano","family":"Comisso","sequence":"additional","affiliation":[{"name":"Department of Engineering and Architecture, Università degli Studi di Trieste, Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9105-6066","authenticated-orcid":false,"given":"Giulia","family":"Buttazzoni","sequence":"additional","affiliation":[{"name":"Department of Engineering and Architecture, Università degli Studi di Trieste, Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0121-5524","authenticated-orcid":false,"given":"Fulvio","family":"Babich","sequence":"additional","affiliation":[{"name":"Department of Engineering and Architecture, Università degli Studi di Trieste, Trieste, Italy"}]}],"member":"263","reference":[{"doi-asserted-by":"publisher","key":"ref1","DOI":"10.1002\/0471200697"},{"doi-asserted-by":"publisher","key":"ref2","DOI":"10.1186\/s13638-015-0511-2"},{"doi-asserted-by":"publisher","key":"ref3","DOI":"10.1109\/TCOMM.2009.11.080479"},{"doi-asserted-by":"publisher","key":"ref4","DOI":"10.1109\/LCOMM.2007.070470"},{"doi-asserted-by":"publisher","key":"ref5","DOI":"10.1109\/LCOMM.2002.806467"},{"doi-asserted-by":"publisher","key":"ref6","DOI":"10.1109\/iwcmc.2012.6314381"},{"doi-asserted-by":"publisher","key":"ref7","DOI":"10.1109\/LCOMM.2008.080815"},{"doi-asserted-by":"publisher","key":"ref8","DOI":"10.1109\/TVT.2008.926072"},{"doi-asserted-by":"publisher","key":"ref9","DOI":"10.1109\/WCL.2012.080112.120232"},{"doi-asserted-by":"publisher","key":"ref10","DOI":"10.1109\/lcomm.2011.032111.102440"},{"doi-asserted-by":"publisher","key":"ref11","DOI":"10.1109\/TWC.2003.814350"},{"doi-asserted-by":"publisher","key":"ref12","DOI":"10.1109\/LWC.2017.2717907"},{"doi-asserted-by":"publisher","key":"ref13","DOI":"10.1109\/TCOMM.2011.012711.100105"},{"volume-title":"Probabilistic Methods of Signal and System Analysis","year":"1998","author":"Cooper","key":"ref14"},{"doi-asserted-by":"publisher","key":"ref15","DOI":"10.1109\/TIT.2010.2043769"},{"doi-asserted-by":"publisher","key":"ref16","DOI":"10.12988\/ams.2014.45338"},{"doi-asserted-by":"publisher","key":"ref17","DOI":"10.2307\/2346231"},{"doi-asserted-by":"publisher","key":"ref18","DOI":"10.2307\/2347681"},{"issue":"9","key":"ref19","first-page":"425","article-title":"A note on approximating the normal distribution function","volume":"2","author":"Aludaat","year":"2008","journal-title":"Appl. Math. Sci."},{"issue":"4","key":"ref20","first-page":"413","article-title":"Alternatives to Hamaker\u2019s approximations to the cumulative normal distribution and its inverse","volume":"37","author":"Lin","year":"1988","journal-title":"J. Roy. Stat. Soc. D Stat."},{"doi-asserted-by":"publisher","key":"ref21","DOI":"10.2307\/2347764"},{"doi-asserted-by":"publisher","key":"ref22","DOI":"10.23919\/SOFTCOM.2019.8903883"},{"year":"2008","author":"Winitzki","article-title":"A handy approximation for the error function and its inverse.","key":"ref23"},{"year":"2012","author":"Soranzo","article-title":"Simply explicitly invertible approximations to 4 decimals of error function and normal cumulative distribution function.","key":"ref24"},{"year":"2012","author":"Soranzo","article-title":"Practical explicitly invertible approximation to 4 decimals of normal cumulative distribution function modifying Winitzki\u2019s approximation of ERF.","key":"ref25"},{"doi-asserted-by":"publisher","key":"ref26","DOI":"10.2307\/2346872"},{"doi-asserted-by":"publisher","key":"ref27","DOI":"10.1016\/0167-9473(93)90248-R"},{"doi-asserted-by":"publisher","key":"ref28","DOI":"10.13189\/ms.2016.040102"},{"doi-asserted-by":"publisher","key":"ref29","DOI":"10.1109\/LCOMM.2018.2832070"},{"doi-asserted-by":"publisher","key":"ref30","DOI":"10.3934\/math.2022648"},{"key":"ref31","volume-title":"Handbook of Mathematical Functions. With Formulas, Graphs, and Mathematical Tables","volume":"55","author":"Abramowitz","year":"1972"},{"volume-title":"The Art of Simulation","year":"1963","author":"Tocher","key":"ref32"},{"doi-asserted-by":"publisher","key":"ref33","DOI":"10.18187\/pjsor.v18i3.4007"},{"doi-asserted-by":"publisher","key":"ref34","DOI":"10.18187\/pjsor.v17i2.3556"},{"doi-asserted-by":"publisher","key":"ref35","DOI":"10.2307\/2346737"},{"doi-asserted-by":"publisher","key":"ref36","DOI":"10.2307\/2347972"},{"doi-asserted-by":"publisher","key":"ref37","DOI":"10.1145\/361932.361949"},{"doi-asserted-by":"publisher","key":"ref38","DOI":"10.2307\/2347061"},{"doi-asserted-by":"publisher","key":"ref39","DOI":"10.2307\/2529920"},{"doi-asserted-by":"publisher","key":"ref40","DOI":"10.1016\/j.jmaa.2014.05.034"},{"doi-asserted-by":"publisher","key":"ref41","DOI":"10.2307\/2331957"},{"doi-asserted-by":"publisher","key":"ref42","DOI":"10.1109\/MILCOM.1991.258319"},{"year":"2023","author":"Temme","article-title":"Error functions, Dawson\u2019s and Fresnel integrals.","key":"ref43"},{"doi-asserted-by":"publisher","key":"ref44","DOI":"10.1016\/j.dsp.2022.103563"},{"doi-asserted-by":"publisher","key":"ref45","DOI":"10.1109\/COMST.2019.2907065"},{"doi-asserted-by":"publisher","key":"ref46","DOI":"10.1109\/TCOMM.2011.072011.100049"},{"doi-asserted-by":"publisher","key":"ref47","DOI":"10.1214\/aoms\/1177729330"},{"volume-title":"Digital Communications","year":"2000","author":"Proakis","key":"ref48"},{"doi-asserted-by":"publisher","key":"ref49","DOI":"10.14711\/spcol\/b718972"},{"volume-title":"Principles of Communication Engineering","year":"1965","author":"Wozencraft","key":"ref50"},{"doi-asserted-by":"publisher","key":"ref51","DOI":"10.1214\/aoms\/1177731721"},{"doi-asserted-by":"publisher","key":"ref52","DOI":"10.1093\/biomet\/63.2.401"},{"doi-asserted-by":"publisher","key":"ref53","DOI":"10.1109\/26.35381"},{"doi-asserted-by":"publisher","key":"ref54","DOI":"10.1016\/j.jmaa.2007.09.063"},{"doi-asserted-by":"publisher","key":"ref55","DOI":"10.1109\/vetecs.2006.1683318"},{"doi-asserted-by":"publisher","key":"ref56","DOI":"10.1109\/ISIT.2006.261952"},{"doi-asserted-by":"publisher","key":"ref57","DOI":"10.1109\/TIT.1975.1055327"},{"doi-asserted-by":"publisher","key":"ref58","DOI":"10.1007\/978-3-642-40607-2_8"},{"doi-asserted-by":"publisher","key":"ref59","DOI":"10.1007\/978-3-642-40607-2_8"},{"doi-asserted-by":"publisher","key":"ref60","DOI":"10.1214\/aoms\/1177730951"},{"key":"ref61","first-page":"12","article-title":"Remarks on computing the probability integral in one and two dimensions","volume-title":"Proc. Symp. Math. Stat. Probab.","author":"P\u00f3lya"},{"doi-asserted-by":"publisher","key":"ref62","DOI":"10.1093\/biomet\/38.3-4.475"},{"doi-asserted-by":"publisher","key":"ref63","DOI":"10.1017\/9781009004091"},{"doi-asserted-by":"publisher","key":"ref64","DOI":"10.1515\/9781400875597"},{"volume-title":"Platonis Opera","year":"1903","author":"Burnet","key":"ref65"},{"key":"ref66","first-page":"213","volume-title":"Theoria Motus Corporum Celestium","author":"Gauss","year":"2023"},{"doi-asserted-by":"publisher","key":"ref67","DOI":"10.1214\/aoms\/1177731611"},{"doi-asserted-by":"publisher","key":"ref68","DOI":"10.2307\/2333443"},{"doi-asserted-by":"publisher","key":"ref69","DOI":"10.1201\/b16720"},{"doi-asserted-by":"publisher","key":"ref70","DOI":"10.1109\/DASC\/PiCom\/DataCom\/CyberSciTec.2018.00-22"},{"volume-title":"Digital Communications","year":"2008","author":"Proakis","key":"ref71"},{"doi-asserted-by":"publisher","key":"ref72","DOI":"10.2307\/2683918"},{"doi-asserted-by":"publisher","key":"ref73","DOI":"10.5755\/j01.eie.26.5.26012"},{"doi-asserted-by":"publisher","key":"ref74","DOI":"10.1049\/el.2019.1349"},{"doi-asserted-by":"publisher","key":"ref75","DOI":"10.3390\/info12050212"},{"doi-asserted-by":"publisher","key":"ref76","DOI":"10.1109\/LCOMM.2018.2886261"},{"doi-asserted-by":"publisher","key":"ref77","DOI":"10.1007\/BF02124750"},{"doi-asserted-by":"publisher","key":"ref78","DOI":"10.1080\/10652460802332342"},{"doi-asserted-by":"publisher","key":"ref79","DOI":"10.1049\/el.2018.0478"},{"doi-asserted-by":"publisher","key":"ref80","DOI":"10.1080\/00401706.1967.10490512"},{"year":"2015","author":"Boiroju","article-title":"Simple approximations to Gaussian Q-function.","key":"ref81"},{"year":"2009","author":"Zogheib","article-title":"Approximations of the standard normal distribution.","key":"ref82"},{"doi-asserted-by":"publisher","key":"ref83","DOI":"10.1109\/VETECS.2011.5956392"},{"doi-asserted-by":"publisher","key":"ref84","DOI":"10.1016\/j.dsp.2022.103800"},{"doi-asserted-by":"publisher","key":"ref85","DOI":"10.1016\/0167-4730(91)90052-B"},{"year":"2013","author":"Mastin","article-title":"Log-quadratic bounds for the Gaussian Q-function.","key":"ref86"},{"doi-asserted-by":"publisher","key":"ref87","DOI":"10.1109\/ISWCS.2010.5624374"},{"doi-asserted-by":"publisher","key":"ref88","DOI":"10.1090\/S0025-5718-1977-0423761-X"},{"doi-asserted-by":"publisher","key":"ref89","DOI":"10.1145\/2330163.2330275"},{"key":"ref90","first-page":"1087","article-title":"Simplified bounds for the complementary error function; application to the performance evaluation of signal-processing systems","volume-title":"Proc. EUSIPCO","author":"Ermolova"},{"issue":"2","key":"ref91","first-page":"1","article-title":"A new approximation to standard normal distribution function","volume":"6","author":"Abderrahmane","year":"2017","journal-title":"J. Appl. Comput. Math."},{"issue":"5","key":"ref92","first-page":"1","article-title":"Two new approximations to standard normal distribution function","volume":"5","author":"Abderrahmane","year":"2016","journal-title":"J. Appl. Comput. Math."},{"doi-asserted-by":"publisher","key":"ref93","DOI":"10.3758\/BF03203732"},{"doi-asserted-by":"publisher","key":"ref94","DOI":"10.1109\/TCOM.1979.1094433"},{"doi-asserted-by":"publisher","key":"ref95","DOI":"10.3926\/jiem.2009.v2n1.p114-127"},{"key":"ref96","volume-title":"Continuous Univariate Distributions","volume":"2","author":"Johnson","year":"1995"},{"year":"1990","author":"Divgi","article-title":"Approximations for three statistical functions","key":"ref97"},{"doi-asserted-by":"publisher","key":"ref98","DOI":"10.1080\/03610926.2018.1563166"},{"doi-asserted-by":"publisher","key":"ref99","DOI":"10.22237\/jmasm\/1146457260"},{"doi-asserted-by":"publisher","key":"ref100","DOI":"10.2307\/2974857"},{"doi-asserted-by":"publisher","key":"ref101","DOI":"10.1093\/biomet\/67.3.675"},{"doi-asserted-by":"publisher","key":"ref102","DOI":"10.1155\/2012\/124029"},{"doi-asserted-by":"publisher","key":"ref103","DOI":"10.1016\/S0096-3003(01)00015-7"},{"doi-asserted-by":"publisher","key":"ref104","DOI":"10.23919\/SoftCOM52868.2021.9559107"},{"doi-asserted-by":"publisher","key":"ref105","DOI":"10.21553\/rev-jec.92"},{"doi-asserted-by":"publisher","key":"ref106","DOI":"10.3758\/BF03200956"},{"year":"2012","author":"C\u00f4t\u00e9","article-title":"A Chernofftype lower bound for the Gaussian Q-function.","key":"ref107"},{"volume-title":"Teoria Generale Delle Equazioni, In Cui Si Dimostra Impossibile La Soluzione Algebrica Delle Equazioni Generali Di Grado Superiore Al Quarto","year":"1799","author":"Ruffini","key":"ref108"},{"volume-title":"Algebra for the Practical Man","year":"1968","author":"Thompson","key":"ref109"},{"doi-asserted-by":"publisher","key":"ref110","DOI":"10.2307\/3621149"}],"container-title":["IEEE Open Journal of the Communications Society"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/8782661\/10008219\/10318209.pdf?arnumber=10318209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T23:09:33Z","timestamp":1703027373000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10318209\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"references-count":110,"URL":"https:\/\/doi.org\/10.1109\/ojcoms.2023.3332838","relation":{},"ISSN":["2644-125X"],"issn-type":[{"type":"electronic","value":"2644-125X"}],"subject":[],"published":{"date-parts":[[2023]]}}}