{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:07:59Z","timestamp":1773148079486,"version":"3.50.1"},"reference-count":12,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"vor","delay-in-days":4213,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Trans Emerging Tel Tech"],"published-print":{"date-parts":[[1997,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For estimating the states or outputs of a Markov process, the symbol\u2010by\u2010symbol maximum a posteriori (MAP) algorithm is optimal. However, this algorithm, even in its recursive form, poses technical difficulties because of numerical representation problems, the necessity of non\u2010linear functions and a high number of additions and multiplications. MAP like algorithms operating in the logarithmic domain presented in the past solve the numerical problem and reduce the computational complexity, but are suboptimal especially at low<jats:italic>SNR<\/jats:italic>(a common example is the Max\u2010Log\u2010MAP because of its use of the max function). A further simplification yields the soft\u2010output Viterbi algorithm (SOVA). In this paper, we present a Log\u2010MAP algorithm that avoids the approximations in the Max\u2010Log\u2010MAP algorithm and hence is equivalent to the true MAP, but without its major disadvantages. We compare the (Log\u2010)MAP, Max\u2010Log\u2010MAP and SOVA from a theoretical point of view to illuminate their commonalities and differences. As a practical example, we consider Turbo decoding, and we also demonstrate the practical suitability of the Log\u2010MAP by including quantization effects. The SOVA is, at 10<jats:sup>\u22124<\/jats:sup>, approximately 0.7 dB inferior to the (Log\u2010)MAP, the Max\u2010Log\u2010MAP lying roughly in between. The channel capacities of the three algorithms \u2010when employed in a Turbo decoder\u2010 are evaluated numerically.<\/jats:p>","DOI":"10.1002\/ett.4460080202","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T13:37:31Z","timestamp":1221226651000},"page":"119-125","source":"Crossref","is-referenced-by-count":400,"title":["Optimal and sub\u2010optimal maximum a posteriori algorithms suitable for turbo decoding"],"prefix":"10.1002","volume":"8","author":[{"given":"Patrick","family":"Robertson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Hoeher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanuelle","family":"Villebrun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1974.1055186"},{"key":"e_1_2_1_3_2","unstructured":"J.Hagenauer P.Hoeher:A Viterbi algorithm with soft\u2010decision outputs and its applications. In: Proc. GLOBECOM \u203289 November1989 p.1680\u20131686."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCOMM.1994.582868"},{"key":"e_1_2_1_5_2","unstructured":"W.Koch A.Baier:Optimum and sub\u2010optimum detection of coded data disturbed by time\u2010varying intersymbol interference. In: Proc. GLOBECOM \u203290 December1990 p.1679\u20131684."},{"key":"e_1_2_1_6_2","unstructured":"J.Petersen:Implementierungsaspekte zur Symbol\u2010by\u2010Symbol MAP Decodierung von Faltungscodes. In: ITG\u2010Fachbericht 130 October1994 p.41\u201348."},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"C.Berrou A.Glavieux P.Thitimajshima:Near Shannon limit error\u2010correcting coding and decoding: Turbo\u2010codes. In: Proc. ICC \u203293 May1993 p.1064\u20131070.","DOI":"10.1109\/ICC.1993.397441"},{"key":"e_1_2_1_8_2","unstructured":"J.Hagenauer P.Robertson L.Papke:Iterative (\u201cTurbo\u201d) decoding of systematic convolutional codes with the MAP and SOVA algorithms. In: ITG\u2010Fachbericht 130 October1994 p.21\u201329."},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"P.Robertson:Illuminating the structures of code and decoder for parallel concatenated recursive systematic (turbo) codes. In: Proc. GLOBECOM \u203294. December1994 p.1298\u20131303.","DOI":"10.1109\/GLOCOM.1994.512991"},{"key":"e_1_2_1_10_2","unstructured":"E.Villebrun:Turbo\u2010decoding with close\u2010to\u2010optimal MAP algorithms. Diploma thesis TU Munich September1994."},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"P.Robertson E.Villebrun P.Hoeher:A comparison of optimal and sub\u2010optimal MAP decoding algorithms operating in the log domain. In: Proc. ICC 95 June1995 p.1009\u20131013.","DOI":"10.1109\/ICC.1995.524253"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1973.9030"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/26.380096"}],"container-title":["European Transactions on Telecommunications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fett.4460080202","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/ett.4460080202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,31]],"date-time":"2025-01-31T22:36:38Z","timestamp":1738362998000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/ett.4460080202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,3]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1997,3]]}},"alternative-id":["10.1002\/ett.4460080202"],"URL":"https:\/\/doi.org\/10.1002\/ett.4460080202","archive":["Portico"],"relation":{},"ISSN":["1124-318X","1541-8251"],"issn-type":[{"value":"1124-318X","type":"print"},{"value":"1541-8251","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,3]]}}}