{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:41:55Z","timestamp":1761745315820,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T00:00:00Z","timestamp":1601596800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T00:00:00Z","timestamp":1601596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"National Research Grants - ARUT of the TUIASI","award":["GnaC2018_39"],"award-info":[{"award-number":["GnaC2018_39"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Telecommun Syst"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s11235-020-00723-4","type":"journal-article","created":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T21:02:48Z","timestamp":1601672568000},"page":"423-447","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Upper bounds on the minimum distance for turbo codes using CPP interleavers"],"prefix":"10.1007","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1697-6406","authenticated-orcid":false,"given":"Lucian","family":"Trifina","sequence":"first","affiliation":[]},{"given":"Daniela","family":"Tarniceriu","sequence":"additional","affiliation":[]},{"given":"Jonghoon","family":"Ryu","sequence":"additional","affiliation":[]},{"given":"Ana-Mirela","family":"Rotopanescu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,2]]},"reference":[{"issue":"3","key":"723_CR1","doi-asserted-by":"publisher","first-page":"2309","DOI":"10.1109\/comst.2019.2893851","volume":"21","author":"S Shao","year":"2019","unstructured":"Shao, S., Hailes, P., Wang, Y.-Y., Wu, J.-Y., Maunder, R. G., Al-Hashimi, M., et al. (2019). Survey of turbo, LDPC, and polar decoder ASIC implementations. IEEE Communications Surveys and Tutorials, 21(3), 2309\u20132333. https:\/\/doi.org\/10.1109\/comst.2019.2893851.","journal-title":"IEEE Communications Surveys and Tutorials"},{"issue":"4","key":"723_CR2","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1007\/s11235-019-00630-3","volume":"73","author":"K Arora","year":"2020","unstructured":"Arora, K., Singh, J., & Randhawa, Y. S. (2020). A survey on channel coding techniques for 5G wireless networks. Telecommunication Systems, 73(4), 637\u2013663. https:\/\/doi.org\/10.1007\/s11235-019-00630-3.","journal-title":"Telecommunication Systems"},{"key":"723_CR3","doi-asserted-by":"publisher","unstructured":"Berrou, C., Glavieux, A., & Thitimajshima, P. (1993). Near Shannon limit error-correcting coding and decoding: Turbo-codes. In Proceedings of IEEE international conference on communications (ICC 1993), Geneva, Switzerland, (Vol. 2, pp. 1064\u20131070). https:\/\/doi.org\/10.1109\/icc.1993.397441.","DOI":"10.1109\/icc.1993.397441"},{"issue":"18","key":"723_CR4","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1049\/el:19961141","volume":"32","author":"DJC MacKay","year":"1996","unstructured":"MacKay, D. J. C., & Neal, R. M. (1996). Near Shannon limit performance of low density parity check codes. Electronics Letters, 32(18), 457\u2013458. https:\/\/doi.org\/10.1049\/el:19961141.","journal-title":"Electronics Letters"},{"issue":"7","key":"723_CR5","doi-asserted-by":"publisher","first-page":"3051","DOI":"10.1109\/tit.2009.2021379","volume":"55","author":"E Arikan","year":"2009","unstructured":"Arikan, E. (2009). Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Transactions on Information Theory, 55(7), 3051\u20133073. https:\/\/doi.org\/10.1109\/tit.2009.2021379.","journal-title":"IEEE Transactions on Information Theory"},{"key":"723_CR6","doi-asserted-by":"publisher","unstructured":"Crozier, S., & Guinand, P. (2001). High-performance low-memory interleaver banks for turbo-codes. In Proceedings of IEEE 54th vehicular technology conference (VTC 2001 Fall), Atlantic City, NJ, USA (Vol. 4, pp. 2394\u20132398). https:\/\/doi.org\/10.1109\/vtc.2001.957178.","DOI":"10.1109\/vtc.2001.957178"},{"key":"723_CR7","doi-asserted-by":"publisher","unstructured":"Berrou, C., Saoter, Y., Douillard, C., Kerouedan, S., & Jezequel, M. (2004). Designing good permutations for turbo codes: Towards a single model. In Proceedings of IEEE international conference on communications (ICC\u201904), Paris, France (Vol. 1, pp. 341\u2013345). https:\/\/doi.org\/10.1109\/icc.2004.1312507.","DOI":"10.1109\/icc.2004.1312507"},{"issue":"1","key":"723_CR8","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1109\/tit.2004.839478","volume":"51","author":"J Sun","year":"2005","unstructured":"Sun, J., & Takeshita, O. Y. (2005). Interleavers for turbo codes using permutation polynomials over integer rings. IEEE Transactions on Information Theory, 51(1), 101\u2013119. https:\/\/doi.org\/10.1109\/tit.2004.839478.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"723_CR9","doi-asserted-by":"publisher","first-page":"2116","DOI":"10.1109\/tit.2005.864450","volume":"53","author":"OY Takeshita","year":"2007","unstructured":"Takeshita, O. Y. (2007). Permutation polynomial interleavers: An algebraic-geometric perspective. IEEE Transactions on Information Theory, 53(6), 2116\u20132132. https:\/\/doi.org\/10.1109\/tit.2005.864450.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"723_CR10","doi-asserted-by":"publisher","first-page":"3707","DOI":"10.1109\/TIT.2011.2133610","volume":"57","author":"E Rosnes","year":"2011","unstructured":"Rosnes, E., & i Amat, A. G. (2011). Performance analysis of 3-D turbo codes. IEEE Transactions on Information Theory, 57(6), 3707\u20133720. https:\/\/doi.org\/10.1109\/TIT.2011.2133610.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"12","key":"723_CR11","doi-asserted-by":"publisher","first-page":"3760","DOI":"10.1587\/transcom.e95.b.3760","volume":"E95\u2013B","author":"J Ryu","year":"2012","unstructured":"Ryu, J. (2012). Permutation polynomials of higher degrees for turbo code interleavers. IEICE Transactions on Communications, E95\u2013B(12), 3760\u20133762. https:\/\/doi.org\/10.1587\/transcom.e95.b.3760.","journal-title":"IEICE Transactions on Communications"},{"issue":"7","key":"723_CR12","doi-asserted-by":"publisher","first-page":"4781","DOI":"10.1109\/tit.2012.2192095","volume":"58","author":"E Rosnes","year":"2012","unstructured":"Rosnes, E. (2012). On the minimum distance of turbo codes with quadratic permutation polynomial interleavers. IEEE Transactions on Information Theory, 58(7), 4781\u20134795. https:\/\/doi.org\/10.1109\/tit.2012.2192095.","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"723_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11277-012-0557-y","volume":"69","author":"L Trifina","year":"2013","unstructured":"Trifina, L., & Tarniceriu, D. (2013). Analysis of cubic permutation polynomials for turbo codes. Wireless Personal Communications, 69(1), 1\u201322. https:\/\/doi.org\/10.1007\/s11277-012-0557-y.","journal-title":"Wireless Personal Communications"},{"issue":"10","key":"723_CR14","doi-asserted-by":"publisher","first-page":"1550","DOI":"10.1016\/j.aeue.2015.06.007","volume":"69","author":"J Ryu","year":"2015","unstructured":"Ryu, J., Trifina, L., & Balta, H. (2015). The limitation of permutation polynomial interleavers for turbo codes and a scheme for dithering permutation polynomials. AEU International Journal of Electronics and Communications, 69(10), 1550\u20131556. https:\/\/doi.org\/10.1016\/j.aeue.2015.06.007.","journal-title":"AEU International Journal of Electronics and Communications"},{"key":"723_CR15","doi-asserted-by":"publisher","unstructured":"Garzon-Bohorquez, R., Abdel Nour, C., & Douillard, C. (2016). Improving turbo codes for 5G with parity puncture-constrained interleavers. In Proceedings of 9-th international symposium on turbo codes & iterative information processing (ISTC 2016), Brest, France (pp. 151\u2013155). https:\/\/doi.org\/10.1109\/ISTC.2016.7593095.","DOI":"10.1109\/ISTC.2016.7593095"},{"issue":"2","key":"723_CR16","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1109\/TCOMM.2016.2628744","volume":"65","author":"C Trifina","year":"2017","unstructured":"Trifina, C., & Tarniceriu, D. (2017). On the equivalence of cubic permutation polynomial and ARP interleavers for turbo codes. IEEE Transactions on Communications, 65(2), 473\u2013485. https:\/\/doi.org\/10.1109\/TCOMM.2016.2628744.","journal-title":"IEEE Transactions on Communications"},{"key":"723_CR17","doi-asserted-by":"publisher","unstructured":"Trifina, L., Ryu, J., & Tarniceriu, D. (2017). Up to five degree permutation polynomial interleavers for short length LTE turbo codes with optimum minimum distance. In Proceedings of IEEE international symposium on signals, circuits and systems (ISSCS 2017), Iasi, Romania. https:\/\/doi.org\/10.1109\/isscs.2017.8034883.","DOI":"10.1109\/isscs.2017.8034883"},{"issue":"5","key":"723_CR18","doi-asserted-by":"publisher","first-page":"1833","DOI":"10.1109\/tcomm.2017.2783971","volume":"66","author":"R Garzon-Bohorquez","year":"2018","unstructured":"Garzon-Bohorquez, R., Abdel Nour, C., & Douillard, C. (2018). Protograph-based interleavers for punctured turbo codes. IEEE Transactions on Communications, 66(5), 1833\u20131844. https:\/\/doi.org\/10.1109\/tcomm.2017.2783971.","journal-title":"IEEE Transactions on Communications"},{"issue":"2","key":"723_CR19","doi-asserted-by":"publisher","first-page":"e3450","DOI":"10.1002\/dac.3450","volume":"31","author":"S Banerjee","year":"2018","unstructured":"Banerjee, S., & Chattopadhyay, S. (2018). Evaluation of system performance by adding a fourth dimension to turbo code. Journal of Communication Systems, 31(2), e3450. https:\/\/doi.org\/10.1002\/dac.3450.","journal-title":"Journal of Communication Systems"},{"issue":"4","key":"723_CR20","doi-asserted-by":"publisher","first-page":"2077","DOI":"10.1007\/s11277-019-06510-y","volume":"108","author":"S Banerjee","year":"2019","unstructured":"Banerjee, S., & Chattopadhyay, S. (2019). Performance analysis of four dimensional turbo code (4D-TC) using moment based simplified augmented state diagram (MSASD) approach: Extension to LTE system. Wirellers Personal Communications, 108(4), 2077\u20132102. https:\/\/doi.org\/10.1007\/s11277-019-06510-y.","journal-title":"Wirellers Personal Communications"},{"issue":"5\u20136","key":"723_CR21","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1007\/s00779-019-01295-0","volume":"23","author":"S Banerjee","year":"2019","unstructured":"Banerjee, S., & Chattopadhyay, S. (2019). Superposition modulation-based new structure of four-dimensional turbo code (4D-TC) using modified interleaver and its application in WiMAX & LTE systems. Personal and Ubiquitous Computing, 23(5\u20136), 943\u2013959. https:\/\/doi.org\/10.1007\/s00779-019-01295-0.","journal-title":"Personal and Ubiquitous Computing"},{"issue":"1","key":"723_CR22","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1109\/LWC.2014.2367517","volume":"4","author":"R Garzon-Bohorquez","year":"2015","unstructured":"Garzon-Bohorquez, R., Abdel Nour, C., & Douillard, C. (2015). On the equivalence of interleavers for turbo codes. IEEE Wireless Communications Letters, 4(1), 58\u201361. https:\/\/doi.org\/10.1109\/LWC.2014.2367517.","journal-title":"IEEE Wireless Communications Letters"},{"issue":"7","key":"723_CR23","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1109\/lcomm.2006.1673009","volume":"10","author":"Y-L Chen","year":"2006","unstructured":"Chen, Y.-L., Ryu, J., & Takeshita, O. Y. (2006). A simple coefficient test for cubic permutation polynomials over integer rings. IEEE Communications Letters, 10(7), 549\u2013551. https:\/\/doi.org\/10.1109\/lcomm.2006.1673009.","journal-title":"IEEE Communications Letters"},{"issue":"12","key":"723_CR24","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1109\/lcomm.2007.071129","volume":"11","author":"H Zhao","year":"2007","unstructured":"Zhao, H., & Fan, P. (2007). A note on \u201cA simple coefficient test for cubic permutation polynomials over integer rings\u201d. IEEE Communications Letters, 11(12), 991. https:\/\/doi.org\/10.1109\/lcomm.2007.071129.","journal-title":"IEEE Communications Letters"},{"issue":"11","key":"723_CR25","doi-asserted-by":"publisher","first-page":"1565","DOI":"10.1016\/j.aeue.2016.09.006","volume":"70","author":"L Trifina","year":"2016","unstructured":"Trifina, L., & Tarniceriu, D. (2016). A coefficient test for fourth degree permutation polynomials over integer rings. AEU International Journal of Electronics and Communications, 70(11), 1565\u20131568. https:\/\/doi.org\/10.1016\/j.aeue.2016.09.006.","journal-title":"AEU International Journal of Electronics and Communications"},{"key":"723_CR26","doi-asserted-by":"publisher","first-page":"37893","DOI":"10.1109\/ACCESS.2018.2854373","volume":"6","author":"L Trifina","year":"2018","unstructured":"Trifina, L., & Tarniceriu, D. (2018). A coefficient test for quintic permutation polynomials over integer rings. IEEE Access, 6, 37893\u201337909. https:\/\/doi.org\/10.1109\/ACCESS.2018.2854373.","journal-title":"IEEE Access"},{"issue":"5","key":"723_CR27","doi-asserted-by":"publisher","first-page":"3097","DOI":"10.1016\/j.jfranklin.2020.02.031","volume":"357","author":"L Trifina","year":"2020","unstructured":"Trifina, L., Tarniceriu, D., Ryu, J., & Rotopanescu, A.-M. (2020). Some lengths for which CPP interleavers have weaker minimum distances than QPP interleavers. Journal of the Franklin Institute, 357(5), 3097\u20133112. https:\/\/doi.org\/10.1016\/j.jfranklin.2020.02.031.","journal-title":"Journal of the Franklin Institute"},{"issue":"1","key":"723_CR28","doi-asserted-by":"publisher","first-page":"78","DOI":"10.3390\/e22010078","volume":"22","author":"L Trifina","year":"2020","unstructured":"Trifina, L., Tarniceriu, D., Ryu, J., & Rotopanescu, A.-M. (2020). Lengths for which fourth degree PP interleavers lead to weaker performances compared to quadratic and cubic PP interleavers. Entropy, 22(1), 78. https:\/\/doi.org\/10.3390\/e22010078.","journal-title":"Entropy"},{"key":"723_CR29","unstructured":"3GPP TS 36.212 V8.3.0, 3rd Generation Partnership Project, Multiplexing and channel coding (Release 8), 2008. [Online]. Retrieved July 23, 2009 from http:\/\/www.etsi.org."},{"key":"723_CR30","unstructured":"Ould-Cheikh-Mouhamedou, Y., Crozier, S., Guinand, P., & Kabal, P. (2005). Comparison of distance measurement methods for turbo codes. In Proceedings of 9-th Canadian workshop on information theory (CWIT\u201905), Montreal, Canada (pp. 36\u201339)."},{"issue":"9","key":"723_CR31","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1002\/dac.2735","volume":"28","author":"Y Ould-Cheikh-Mouhamedou","year":"2015","unstructured":"Ould-Cheikh-Mouhamedou, Y. (2015). Reducing the complexity of distance measurement methods for circular turbo codes that use structured interleavers. International Journal of Communication Systems, 28(9), 1572\u20131579. https:\/\/doi.org\/10.1002\/dac.2735.","journal-title":"International Journal of Communication Systems"},{"key":"723_CR32","unstructured":"Guinand, P., & Lodge, J. (1994). Trellis termination for turbo encoders. In Proceedings of 17th Biennial symposium on communications, Queen\u2019s University, Kingston, Canada (pp. 389\u2013392)."},{"key":"723_CR33","doi-asserted-by":"publisher","unstructured":"Trifina, L., Tarniceriu, D., Ryu, J., & Rotopanescu, A.-M. (2019). Nonlinearity degree for CPP, 4-PP, and 5-PP interleavers for turbo codes. In Proceedings of international conference on electronics, computers and artificial intelligence (ECAI), Pitesti, Romania. https:\/\/doi.org\/10.1109\/ECAI46879.2019.9042119.","DOI":"10.1109\/ECAI46879.2019.9042119"},{"issue":"3","key":"723_CR34","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1109\/LCOMM.2010.03.091695","volume":"14","author":"H Zhao","year":"2010","unstructured":"Zhao, H., Fan, P., & Tarokh, V. (2010). On the equivalence of interleavers for turbo codes using quadratic permutation polynomials over integer rings. IEEE Communications Letters, 14(3), 236\u2013238. https:\/\/doi.org\/10.1109\/LCOMM.2010.03.091695.","journal-title":"IEEE Communications Letters"},{"key":"723_CR35","volume-title":"An Introduction to the Theory of Numbers","author":"GH Hardy","year":"1975","unstructured":"Hardy, G. H., & Wright, E. M. (1975). An Introduction to the Theory of Numbers (4th ed.). Oxford: Oxford University Press.","edition":"4"}],"container-title":["Telecommunication Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11235-020-00723-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11235-020-00723-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11235-020-00723-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,2]],"date-time":"2021-10-02T01:35:52Z","timestamp":1633138552000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11235-020-00723-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,2]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["723"],"URL":"https:\/\/doi.org\/10.1007\/s11235-020-00723-4","relation":{},"ISSN":["1018-4864","1572-9451"],"issn-type":[{"type":"print","value":"1018-4864"},{"type":"electronic","value":"1572-9451"}],"subject":[],"published":{"date-parts":[[2020,10,2]]},"assertion":[{"value":"20 September 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 October 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"On behalf of all authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}