{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T18:33:18Z","timestamp":1649097198668},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,12,1]],"date-time":"2013-12-01T00:00:00Z","timestamp":1385856000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>This paper presents a new family of turbo codes called multi-non-binary turbo codes (MNBTCs) that generalizes the concept of turbo codes to multi-non-binary (MNB) parallel concatenated convolutional codes (PCCC). An MNBTC incorporates, as component encoders, recursive and systematic multi-non-binary convolutional encoders. The more compact data structure for these encoders confers some advantages on MNBTCs over other types of turbo codes, such as better asymptotic behavior, better convergence, and reduced latency. This paper presents in detail the structure and operation of an MNBTC: MNB encoding, trellis termination, Max-Log-MAP decoding adapted to the MNB case. It also shows an example of MNBTC whose performance is compared with the state-of-the-art turbo code adopted in the DVB-RCS2 standard.<\/jats:p>","DOI":"10.1186\/1687-1499-2013-279","type":"journal-article","created":{"date-parts":[[2013,12,5]],"date-time":"2013-12-05T12:16:42Z","timestamp":1386245802000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Multi-non-binary turbo codes"],"prefix":"10.1186","volume":"2013","author":[{"given":"Horia","family":"Balta","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Catherine","family":"Douillard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Radu","family":"Lucaciu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,5]]},"reference":[{"key":"845_CR1","first-page":"1064","volume":"23\u201326","author":"C Berrou","year":"1993","unstructured":"Berrou C, Glavieux A, Thitimajshima P: Near Shannon limit error-correcting coding and decoding: turbo-codes. In Proceedings of ICC, Geneva May, 1993, 23\u201326: 1064-1070.","journal-title":"In Proceedings of ICC, Geneva"},{"key":"845_CR2","volume-title":"Evolved universal terrestrial radio access (E-UTRA)","author":"ETSI, 3GPP TS 36.212","year":"2010","unstructured":"ETSI, 3GPP TS 36.212: Evolved universal terrestrial radio access (E-UTRA). 2010. (January 2010)http:\/\/www.etsi.org\/deliver\/etsi_ts\/136200_136299\/136212\/08.08.00_60\/ts_136212v080800p.pdf"},{"key":"845_CR3","volume-title":"DVB Interactive Satellite System, Part 2","author":"DVB, European Telecommunications Standards Institute","year":"2011","unstructured":"DVB, European Telecommunications Standards Institute: DVB Interactive Satellite System, Part 2. Lower Layers for Satellite standard, DVB document A155-2; 2011. (March 2011)http:\/\/www.dvb.org\/resources\/public\/standards\/a155-2_DVB-RCS2_Lower_Layers.pdf"},{"key":"845_CR4","volume-title":"Recommendation for space data system standards, synchronization and channel coding","author":"Consultative Committee for Space Data Systems","year":"2011","unstructured":"Consultative Committee for Space Data Systems: Recommendation for space data system standards, synchronization and channel coding. 2011. (August 2011)http:\/\/public.ccsds.org\/publications\/archive\/131x0b2ec1.pdf"},{"issue":"10","key":"845_CR5","doi-asserted-by":"publisher","first-page":"1630","DOI":"10.1109\/TCOMM.2005.857165","volume":"53","author":"C Douillard","year":"2005","unstructured":"Douillard C, Berrou C: Turbo codes with rate-m\/(m + 1) constituent convolutional codes. IEEE Transactions on Communications 2005, 53(10):1630-1638.","journal-title":"IEEE Transactions on Communications"},{"issue":"5","key":"845_CR6","doi-asserted-by":"publisher","first-page":"1209","DOI":"10.1109\/TCOMM.2009.05.050300","volume":"57","author":"M Ferrari","year":"2009","unstructured":"Ferrari M, Bellini S: Rate variable multi-binary turbo codes with controlled error-floor. IEEE Transactions on Communications 2009, 57(5):1209-1214.","journal-title":"IEEE Transactions on Communications"},{"issue":"4","key":"845_CR7","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1109\/4234.664216","volume":"2","author":"J Berkmann","year":"1998","unstructured":"Berkmann J: On turbo decoding of nonbinary codes. IEEE Communications Letters 1998, 2(4):94-96.","journal-title":"IEEE Communications Letters"},{"issue":"9","key":"845_CR8","doi-asserted-by":"publisher","first-page":"1417","DOI":"10.1109\/TCOMM.2005.855019","volume":"53","author":"AC Reid","year":"2005","unstructured":"Reid AC, Gulliver TA, Taylor DP: Rate-1\/2 component codes for nonbinary turbo codes. IEEE Transactions on Communications 2005, 53(9):1417-1422.","journal-title":"IEEE Transactions on Communications"},{"key":"845_CR9","volume-title":"Turbo codes based on time-variant memory-1 convolutional codes over Fq, In IEEE ICC 2011, Kyoto, 5\u20139","author":"G Liva","year":"2011","unstructured":"Liva G, Scalise S, Paolini E, Chiani M: Turbo codes based on time-variant memory-1 convolutional codes over Fq, In IEEE ICC 2011, Kyoto, 5\u20139. June 2011."},{"key":"845_CR10","first-page":"113","volume-title":"Multi-Non-Binary Turbo-Codes From Convolutional to Reed-Solomon Codes, In Scientific Bulletin of Politehnica University of Timisoara, Transactions on Electronics and Communications, Tom 51\u201365 Timisoara","author":"H Balta","year":"2006","unstructured":"Balta H, Kovaci M, de Baynast A, Vl\u0103deanu C, Lucaciu R: Multi-Non-Binary Turbo-Codes From Convolutional to Reed-Solomon Codes, In Scientific Bulletin of Politehnica University of Timisoara, Transactions on Electronics and Communications, Tom 51\u201365 Timisoara. Sept: Romania; 2006:113-118."},{"key":"845_CR11","first-page":"100","volume-title":"Cryptography and Coding, 5th IMA Conference, Lecture Notes in Computer Science number 1025","author":"DJC Mackay","year":"1995","unstructured":"Mackay DJC, Neal RM: Good codes based on very sparse matrices. In Cryptography and Coding, 5th IMA Conference, Lecture Notes in Computer Science number 1025. Edited by: Colin B. Berlin, Germany: Springer; 1995:100-111."},{"issue":"6","key":"845_CR12","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1109\/4234.681360","volume":"2","author":"MC Davey","year":"1998","unstructured":"Davey MC, MacKay DJC: Low-density parity check codes over GF(q). IEEE Communications Letters 1998, 2(6):165-167.","journal-title":"IEEE Communications Letters"},{"issue":"10","key":"845_CR13","doi-asserted-by":"publisher","first-page":"2224","DOI":"10.1109\/LPT.2005.856337","volume":"17","author":"IB Djordjevic","year":"2005","unstructured":"Djordjevic IB, Vasic B: Nonbinary LDPC codes for optical communication systems. IEEE Photonics Technology Letters 2005, 17(10):2224-2226.","journal-title":"IEEE Photonics Technology Letters"},{"key":"845_CR14","first-page":"1019","volume":"26\u201329","author":"G Bosco","year":"2006","unstructured":"Bosco G, Garello R, Mininni F, Baldi M, Chiaraluce F: Non-binary low density parity check codes for satellite communications. In Proceedings of the ISCC, Cagliari, Italy June, 2006, 26\u201329: 1019-1024.","journal-title":"In Proceedings of the ISCC, Cagliari, Italy"},{"key":"845_CR15","volume-title":"Opportunistic adaptive transmission for network coding using nonbinary LDPC codes","author":"G Cocco","year":"2010","unstructured":"Cocco G, Pfletschinger S, Navarro M, Ibars C: Opportunistic adaptive transmission for network coding using nonbinary LDPC codes. EURASIP Journal on Wireless Communications and Networking (2010); 2010. Doi: 10.1155\/2010\/517921"},{"key":"845_CR16","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1186\/1687-1499-2012-55","volume":"2012","author":"A Mourad","year":"2012","unstructured":"Mourad A, Picchi O, Gutierrez I, Luise M: Low complexity soft demapping for non-binary LDPC codes. EURASIP Journal on Wireless Communications and Networking 2012, 2012: 55.","journal-title":"EURASIP Journal on Wireless Communications and Networking"},{"key":"845_CR17","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1186\/1687-1499-2013-18","volume":"2013","author":"A Marinoni","year":"2013","unstructured":"Marinoni A, Savazzi P, Gamba P: Efficient detection and decoding of q-ary LDPC coded signals over partial response channels. EURASIP Journal on Wireless Communications and Networking 2013, 2013: 18.","journal-title":"EURASIP Journal on Wireless Communications and Networking"},{"key":"845_CR18","volume-title":"Linear Systems","author":"T Kailath","year":"1980","unstructured":"Kailath T: Linear Systems. Upper Saddle River: Prentice-Hall; 1980."},{"key":"845_CR19","doi-asserted-by":"publisher","DOI":"10.1109\/9780470544693","volume-title":"Fundamentals of Convolutional Coding","author":"R Johannesson","year":"1999","unstructured":"Johannesson R, Zigangirov KS: Fundamentals of Convolutional Coding. Fundamentals of Convolutional Coding: IEEE Press; 1999."},{"key":"845_CR20","first-page":"343","volume-title":"Turbo decoding with tailbiting trellises In Proc","author":"C Weiss","year":"1998","unstructured":"Weiss C, Bettstetter C, Riedel S, Costello DJ: Turbo decoding with tailbiting trellises In Proc. Electron, Pisa, Italy: IEEE Int. Symp. Signals, Syst; 1998:343-348."},{"key":"845_CR21","first-page":"389","volume-title":"Trellis Termination for Turbo Encoders In Proceedings of the 17th Biennial Symposium on Communications Queen\u2019s University","author":"P Guinand","year":"1994","unstructured":"Guinand P, Lodge J: Trellis Termination for Turbo Encoders In Proceedings of the 17th Biennial Symposium on Communications Queen\u2019s University. ON, Canada: Kingston; May 1994:389-392."},{"issue":"5","key":"845_CR22","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1109\/49.924868","volume":"19","author":"J Hokfelt","year":"2001","unstructured":"Hokfelt J, Edfors O, Maseng T: On the theory and performance of trellis termination methods for turbo codes. IEEE Journal on Selected Areas in Communications 2001, 19(5):838-847.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"2","key":"845_CR23","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1109\/TIT.1974.1055186","volume":"20","author":"LR Bahl","year":"1974","unstructured":"Bahl LR, Cocke J, Jelinek F, Raviv J: Optimal decoding of linear codes for minimising symbol error rate. IEEE Transactions on Information Theory 1974, 20(2):284-287.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"845_CR24","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1002\/ett.4460080202","volume":"8","author":"P Robertson","year":"1997","unstructured":"Robertson P, Hoeher P, Villebrun E: Optimal and suboptimal maximum a posteriori algorithms suitable for turbo decoding. European Trans. Telecommun. 1997, 8(2):119-125.","journal-title":"European Trans. Telecommun"},{"key":"845_CR25","first-page":"1679","volume-title":"Optimum and sub-optimum detection of coded data disturbed by time-varying intersymbol interference, In GLOBECOM\u201990","author":"W Koch","year":"1990","unstructured":"Koch W, Baier A: Optimum and sub-optimum detection of coded data disturbed by time-varying intersymbol interference, In GLOBECOM\u201990. CA, USA: San Diego; December 1990:1679-1684."},{"issue":"23","key":"845_CR26","doi-asserted-by":"publisher","first-page":"1937","DOI":"10.1049\/el:20001357","volume":"36","author":"J Vogt","year":"2000","unstructured":"Vogt J, Finger A: Improving the max-log-MAP turbo decoder. Electronics Letters 2000, 36(23):1937-1939.","journal-title":"Electronics Letters"},{"key":"845_CR27","first-page":"3","volume-title":"New high-spread high-distance interleavers for turbo-codes","author":"SN Crozie","year":"2000","unstructured":"Crozie SN: New high-spread high-distance interleavers for turbo-codes. Commun, Kingston, Canada: 20th Biennial Symp; 2000:3-7."},{"key":"845_CR28","first-page":"341","volume":"1","author":"C Berrou","year":"2004","unstructured":"Berrou C, Saouter Y, Douillard C, Kerou\u00e9dan S, J\u00e9z\u00e9quel M: Designing good permutations for turbo codes: towards a single model. In IEEE International Conference on Communications, Paris, France 2004, 1: 341-345.","journal-title":"In IEEE International Conference on Communications, Paris, France"},{"issue":"1","key":"845_CR29","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1109\/TIT.2004.839478","volume":"51","author":"QJ Sun","year":"2005","unstructured":"Sun QJ, Takeshita OY: Interleavers for turbo codes using permutation polynomials over integer rings. IEEE Trans. Inform. Theory 2005, 51(1):101-119.","journal-title":"IEEE Trans. Inform. Theory"},{"key":"845_CR30","volume-title":"Stopping rules for turbo decoders","author":"A Matache","year":"2000","unstructured":"Matache A, Dolinar S, Pollara F: Stopping rules for turbo decoders. Pasadena, California: TMO Progress Report 42\u2013142, Jet Propulsion Laboratory; 2000."},{"key":"845_CR31","first-page":"5","volume-title":"Information Theory and Reliable Communication","author":"RG Gallager","year":"1968","unstructured":"Gallager RG: Information Theory and Reliable Communication. Wiley, New York; 1968:5-6."},{"issue":"9","key":"845_CR32","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1049\/el.2010.0566","volume":"46","author":"E Boutillon","year":"2010","unstructured":"Boutillon E, Conde-Canencia L: Bubble check: a simplified algorithm for elementary check node processing in extended min-sum non-binary LDPC decoders. Electronic Letter 2010, 46(9):633-634.","journal-title":"Electronic Letter"},{"issue":"10","key":"845_CR33","doi-asserted-by":"publisher","first-page":"6788","DOI":"10.1109\/TIT.2011.2162259","volume":"57","author":"K Kasai","year":"2011","unstructured":"Kasai K, Declercq D, Poulliat C, Sakaniwa K: Multiplicatively repeated non-binary LDPC codes. IEEE Transactions on Information Theory 2011, 57(10):6788-6795.","journal-title":"IEEE Transactions on Information Theory"},{"key":"845_CR34","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1002\/sat.1004","volume":"30","author":"L Costantini","year":"2012","unstructured":"Costantini L, Matuz B, Liva G, Paolini E, Chiani M: Non-binary protograph low-density parity-check codes for space communications. Int. J. Satell. Commun. Network 2012, 30: 43-51.","journal-title":"Int. J. Satell. Commun. Network"},{"key":"845_CR35","first-page":"122","volume":"13\u201315","author":"L Costantini","year":"2010","unstructured":"Costantini L, Matuz B, Liva G, Paolini E, Chiani M: On the Performance of Moderate-Length Non-Binary LDPC Codes for Space Communications, In the 5th Advanced Satellite Multimedia Systems Conference and the 11th Signal Processing for Space Communications Workshop . Cagliari Sept. 2010, 13\u201315: 122-126.","journal-title":"Cagliari"},{"issue":"10","key":"845_CR36","doi-asserted-by":"publisher","first-page":"5314","DOI":"10.1109\/TIT.2010.2059910","volume":"56","author":"L Sassatelli","year":"2010","unstructured":"Sassatelli L, Declercq D: Non-binary Hybrid LDPC Codes. IEEE Transactions on Information Theory 2010, 56(10):5314-5334.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"10","key":"845_CR37","doi-asserted-by":"publisher","first-page":"2644","DOI":"10.1109\/TCSI.2013.2279186","volume":"60","author":"E Boutillon","year":"2013","unstructured":"Boutillon E, Conde-Canencia L, Ghouwayel AA: Design of a GF(64)-LDPC Decoder Based on the EMS Algorithm. IEEE Transactions on Circuits and Systems I 2013, 60(10):2644-2656.","journal-title":"IEEE Transactions on Circuits and Systems I"},{"key":"845_CR38","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1109\/ITW2.2006.323759","volume-title":"IEEE Information Theory Workshop, ITW\u201906 (Chengdu, 2006)","author":"L Sassatelli","year":"2006","unstructured":"Sassatelli L, Declercq D: Non-binary Hybrid LDPC Codes: structure, decoding and optimization. IEEE Information Theory Workshop, ITW\u201906 (Chengdu, 2006) 2006, 71-75. doi: 10.1109\/ITW2.2006.323759"},{"key":"845_CR39","first-page":"199","volume-title":"\u201cThe Minimum Likelihood APP Based Early Stopping Criterion for Multi-Binary Turbo Codes\u201d, In Scientific Bulletin of Politehnica University of Timisoara, Transactions on Electronics and Communications, Tom 51\u201365","author":"H Balta","year":"2006","unstructured":"Balta H, Douillard C, Kovaci M: \u201cThe Minimum Likelihood APP Based Early Stopping Criterion for Multi-Binary Turbo Codes\u201d, In Scientific Bulletin of Politehnica University of Timisoara, Transactions on Electronics and Communications, Tom 51\u201365. Romania: Timisoara; Sept. 2006:199-203."},{"issue":"2","key":"845_CR40","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1109\/18.485714","volume":"42","author":"J Hagenauer","year":"1996","unstructured":"Hagenauer J, Offer E, Papke L: Iterative decoding of binary block and convolutional codes. IEEE Transactions on Information Theory 1996, 42(2):429-445.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"8","key":"845_CR41","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1109\/26.780444","volume":"47","author":"RY Shao","year":"1999","unstructured":"Shao RY, Lin S, Fossorier MPC: Two simple stopping criteria for turbo decoding. IEEE Transactions on Communications 1999, 47(8):1117-1120.","journal-title":"IEEE Transactions on Communications"},{"issue":"10","key":"845_CR42","doi-asserted-by":"publisher","first-page":"1617","DOI":"10.1109\/TCOMM.2003.818099","volume":"51","author":"F Zhai","year":"2003","unstructured":"Zhai F, Fair IJ: Techniques for early stopping and error detection in turbo decoding. IEEE Transactions on Communications 2003, 51(10):1617-1623.","journal-title":"IEEE Transactions on Communications"},{"key":"845_CR43","first-page":"1","volume-title":"Stopping rules for duo-binary turbo codes and application to HomePlug AV","author":"L Guerrieri","year":"2008","unstructured":"Guerrieri L, Veronesi D, Bisaglia P: Stopping rules for duo-binary turbo codes and application to HomePlug AV. New Orleans: In IEEE Global Telecommunications Conference; 2008:1-5. doi: 10.1109\/GLOCOM.2008. ECP.558"},{"issue":"10","key":"845_CR44","doi-asserted-by":"publisher","first-page":"1606","DOI":"10.1049\/iet-com.2008.0579","volume":"3","author":"H Van Khuong","year":"2009","unstructured":"Van Khuong H, Le-Ngoc T: A cooperative turbo coding scheme for wireless fading channels. IET Communications 2009, 3(10):1606-1615.","journal-title":"IET Communications"},{"key":"845_CR45","volume-title":"EURASIP Journal on Wireless Communications and Networking","author":"V Bota","year":"2010","unstructured":"Bota V, ZsA P, Silva A, Teodoro S, Stef MP, Moco A, Botos A, Gameiro A: Combined distributed turbo coding and space frequency block coding techniques. EURASIP Journal on Wireless Communications and Networking 2010. doi: 10.1155\/2010\/327041"},{"issue":"1","key":"845_CR46","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1109\/TWC.2011.110811.110220","volume":"11","author":"F Babich","year":"2012","unstructured":"Babich F, Crismani A: Cooperative coding schemes: design and performance evaluation. IEEE Transactions on Wireless Communications 2012, 11(1):222-235.","journal-title":"IEEE Transactions on Wireless Communications"}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-1499-2013-279.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/1687-1499-2013-279\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-1499-2013-279.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T02:38:48Z","timestamp":1630550328000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/1687-1499-2013-279"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["845"],"URL":"https:\/\/doi.org\/10.1186\/1687-1499-2013-279","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]},"assertion":[{"value":"18 March 2013","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 November 2013","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 December 2013","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"279"}}