Abstract
Performance estimations of various kinds of turbo codes (TCs) and their applications in modern communication systems have been emerged as one of the potential research areas in recent past. In this paper, a modified interleaver-driven binary 4-Dimensional Turbo Code (4D-TC) using superposition modulation (SM) technique has been projected to intensify the minimum hamming distance (MHD). MHD (dmin) of the proposed structure has been amplified by incorporating feedback polynomial in primitive form for a fixed interleaver length. Moreover, improved dmin has further been achieved by introducing a modified interleaver which has been used to ensure scattering and mixing operation on the incoming bits in an appropriate manner. Furthermore, upper bound of the proposed structure has been evaluated and comprehensive asymptotic behavior of the proposed code has been analyzed in terms of dmin by adopting two analytical approaches namely finite length rule and asymptotic spectral shape function. Finally, to prove the superiority of the proposed structure, a comparative study of the BER performance of different forms of TCs have been carried out in WiMAX under numerous fading settings. Moreover a comparative BER analysis has also been done in long term evolution (LTE) system as well.
Similar content being viewed by others
References
Berrou C, Glavieux A, Thitimajshima P (1993) Near Shannon limit error correcting coding and decoding: turbo codes. In: Proceeding of IEEE International Conference on Communications (ICC '93), Geneva, Vol. 2, pp 1064–1070. https://doi.org/10.1109/ICC.1993.397441
DVB (2000) Interaction channel for satellite distribution systems. ETSI EN 301 790, v 1.2.2
DVB (2001) Interaction channel for digital terrestrial television. ETSI EN 301958, v. 1.1.1
IEEE standard for local and metropolitan area networks. IEEE 802.16a, 2003
Benedetto S, Montorsi G (1996) Design of Parallel Concatenated Convolutional Codes. IEEE Trans Commun 44(5):591–600. https://doi.org/10.1109/26.494303
Benedetto S, Montorsi G (1996) Unveiling turbo codes: some results on parallel concatenated coding schemes. IEEE Trans Inf Theory 42(2):409–429. https://doi.org/10.1109/18.485713
Benedetto S, Montorsi G (1996) Serial concatenation of interleaved codes: analytical performance bounds. In: Proceeding of IEEE Global Telecommunications Conference, (GLOBECOM ’96), vol 1, pp 106–110. https://doi.org/10.1109/GLOCOM.1996.594342
Perez LC, Seghers J, Costello DJ (1996) A distance spectrum interpretation of turbo codes. IEEE Trans Inf Theory 42(6):1698–1709. https://doi.org/10.1109/18.556666
Takeshita OY, Collins OM, Massey PC, Costello DJ (1999) A note on asymmetric turbo-codes. IEEE Commun Lett 3(3):69–71. https://doi.org/10.1109/4234.752905
Douillard C, Berrou C (2005) Turbo Codes with Rate-m/ (m + 1) Constituent Convolutional Codes. IEEE Trans Commun 53(10):1630–1638. https://doi.org/10.1109/TCOMM.2005.857165
Berrou C, Graell i Amat A, Ould-Cheikh-Mouhamedou Y, Douillard C, Saouter Y (2007) Adding a rate-1 third dimension to turbo codes. In: Proceedings of IEEE Information Theory Workshop (ITW’07), Lake Taho, CA, pp 156–161. https://doi.org/10.1109/ITW.2007.4313066
Berrou C, Graell i Amat A, Ould-Cheikh-Mouhamedou Y, Saouter Y (2009) Improving the distance properties of turbo codes using a third component code: 3D turbo codes. IEEE Trans Commun 57(9):2505–2509. https://doi.org/10.1109/TCOMM.2009.09.070521
Li J, Narayanan KR, Georghiades CN (2004) Product accumulate codes: A class of codes with near-capacity performance and low decoding complexity. IEEE Trans Inf Theory 50(1):31–46. https://doi.org/10.1109/TIT.2003.821995
Gonzalez H, Berrou C, Kerou’edan S (2004) Serial/parallel (s/p) turbo codes for low error rates. In: Proceedings of IEEE International Conference on Communication (ICC’04), Paris, France, vol 1, pp 346–350. https://doi.org/10.1109/ICC.2004.1312508
Rosnes E, Graell i Amat A (2011) Performance analysis of 3-D turbo codes. IEEE Trans Inf Theory 57(6):3707–3720. https://doi.org/10.1109/TIT.2011.2133610
Kbaier D, Douillard C, Kerouedan S (2012) Analysis of three-dimensional turbo codes. Ann Telecommun, Springer Verlag (Germany) 67(5–6):257–268
Rosnes E, Helmling M, Graell i Amat A (2014) Minimum pseudoweight analysis of 3-dimensional turbo codes. IEEE Trans Commun 62(7):2170–2182. https://doi.org/10.1109/TCOMM.2014.2329690
Sadjadpour HR (2001) Interleaver Design for Multi-Tone Turbo Trellis Coded Modulation Scheme for G.dmt.bis and G.lite.bis. AT&T, ITU-Telecommunication Standardization Sector
Crozier S and Guinand P (2003) Distance upper bounds and true minimum distance results for turbo-codes designed with DRP interleavers. In: Proc. 3rd Int. Symp. Turbo Codes and Related Topics, Brest, France, pp 169–172
Crozier S, Guinand P, Hunt A (2004) Computing the minimum distance of turbo-codes using iterative decoding techniques. In: Proc. 22th Bienn. Symp. Communications, Kingston, ON, Canada, pp 306–308
Berrou C, Kerouédan S, Saouter Y, Douillard C, Jézéquel M (2004) Designing good permutations for turbo codes: Towards a single model. In: Proc. IEEE Int. Conf. Communications (ICC), Paris, France, vol. 1, pp 341–345. https://doi.org/10.1109/ICC.2004.1312507
Sun J, Takeshita OY (2005) Interleavers for turbo codes using permutation polynomials over integer rings. IEEE Trans Inf Theory 51(1):101–119
Takeshita OY (2007) Permutation polynomial interleavers: an algebraic geometric perspective. IEEE Trans Inf Theory 53(6):2116–2132
Rosnes E, Takeshita OY (2006) Optimum distance quadratic permutation polynomial-based interleavers for turbo codes. In: Proc. IEEE Int. Symp. Information Theory (ISIT), Seattle, WA, pp 1988–1992
Nimbalker A, Blankenship TK, Classon B, Fuja TE, Costello DJ Jr (2004) Contention-free interleavers. In: Proc. IEEE Int. Symp. Information Theory (ISIT), Chicago, IL, p 54
Blankenship TK, Classon B, Desai V (2002) High-throughput turbo decoding techniques for 4G. In: Proc. Int. Conf. 3G Wireless and Beyond, San Francisco, CA, pp 137–142
Takeshita OY (Mar. 2006) On maximum contention-free interleavers and permutation polynomials over integer rings. IEEE Trans Inf Theory 52(3):1249–1253
Sason I, Telatar E, Urbanke R (2002) On the asymptotic input-output weight distributions and thresholds of convolutional and turbo-like encoders. IEEE Trans Inf Theory 48(12):3052–3061
Pfister HD, Siegel PH (2003) The serial concatenation of rate-1 codes through uniform random interleavers. IEEE Trans Inf Theory 49(6):1425–1438
Perotti A, Benedetto S (2004) A new upper bound on the minimum distance of turbo codes. IEEE Trans Inf Theory 50(12):2985–2997
Perotti A, Benedetto S (2006) An upper bound on the minimum distance of serially concatenated convolutional codes. IEEE Trans Inf Theory 52(12):5501–5509
Bazzi L, Mahdian M, Spielman DA (2009) The minimum distance of turbo-like codes. IEEE Trans Inf Theory 55(1):6–15. https://doi.org/10.1109/TIT.2008.2008114
Pfister HD (2003) On the Capacity of finite state channels and the analysis of convolutional accumulate- codes. Ph.D. Dissertation, University of California San Diego, San Diego, CA, [Online]. Available:http://www.ece.tamu.edu/~hpfister/research.html
Gallager RG (1963) Low-density parity-check codes. MIT Press, Cambridge, MA
Ravazzi C, Fagnani F (2009) Spectra and minimum distances of repeat multiple-accumulate codes. IEEE Trans Inf Theory 55(11):4905–4924
Kliewer J, Zigangirov KS, Costello DJ Jr (2007) New results on the minimum distance of repeat multiple accumulate codes. In: Proc. 45th Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL
Koller C, Graell i Amat A, Kliewer J, Vatta F, Costello DJ Jr (2008) Hybrid concatenated codes with asymptotically good distance growth. In: Proc. 5th Int. Symp. Turbo Codes and Related Topics, Lausanne, pp 19–24
Hoeher PA, Wo T (Dec. 2011) Superposition modulation: myths and facts. IEEE Commun Mag 49(12):110–116
Meinam S, Chattopadhyay S, Pradhan S (2013) Some studies on different power allocation schemes of superposition modulation. In: Proc. of Int. Conf. on Advances in Computer Science and Application, ACEEE
Banerjee S, Chattopadhyay S, Dey A Improved three dimensional turbo code using superposition modulation techniques: extension to WiMAX system. In: Proceedings of IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics Engineering (UPCON), pp 311–316. https://doi.org/10.1109/UPCON.2016.7894671
Banerjee S, Chattopadhyay S (2017) Evaluation of system performance by adding a fourth dimension to turbo code. Int J Commun Syst, Wiley
Ioannis Ap Chatzigeorgiou (2006) Performance analysis and design of punctured turbo codes. PhD. dissertation
Hokfelt J, Edfors O, Maseng T (1999) Turbo codes: correlated extrinsic information and its impact on iterative decoding performance. Proceeding of IEEE VTC, Houston, Texas
Khandani AK (1998) Group structure of turbo codes with applications to the interleaver design. International Symposium on Information Theory, pp 421
Takeshita OY and Costello Jr DJ (1998) New classes of algebraic interleavers for turbo codes. International Symposium on Information Theory, pp 419
Wang CC (1998) On the performance of turbo code. In: IEEE Military Communications Conference. Proceedings. MILCOM 98, vol 3
Banerjee S, Chattopadhyay S (2017) Power optimization of three dimensional turbo code using a novel modified symbiotic organism search (MSOS) algorithm. Wirel Pers Commun, Springer. https://doi.org/10.1007/s11277-016-3586-0
Dolinar S and Divsalar D (1995) Weight distributions for Turbo codes using random and nonrandom permutations. TDA Progress Report 42-122
Huang F-h (1997) Evaluation of soft output decoding for turbo codes. Master of Science dissertation
Kayani A, Aziz K, Khattak S (2014) Optimising the activation cycle of turbo decoders using three-dimensional extrinsic information transfer charts. IET Commun 8(15):2706–2712. https://doi.org/10.1049/ietcom.2013.1031
Luiz MG, Demo SR, Cecilio P, Eduardo PM, Uchoa-Filho Bartolomeu F, Isaac B (2013) Turbo decoding using the sectionalized minimal trellis of the constituent code: performance-complexity trade-off. IEEE Trans Commun 61(9)
Benedetto S, Montorsi G (1998) Serial concatenation of interleaved codes: performance analysis, design and iterative decoding. IEEE Trans Inf Theory 44(3):909–926
Valenti MC, Sun J (2001) The UMTS turbo code and an efficient decoder implementation suitable for software-defined radios. Int J Wireless Inf Networks; 8(4): (© 2002)
IEEE standard for local and Metropolitan area networks, part 16: air interface for broadband wireless access systems. IEEE Std 802.16™-2009
Roca (2007) Implementation of WiMax simulator in Simulink, Vienna
Sacchi OZ (2007) Objeet-oriented model of SDR library for WiMax/ UMTS system baseband level. Technical Report, University of Trento, Department of Information and Communication Technology
Sahoo B, Prasad RR, Samundiswary P (2013) BER analysis of mobile WiMAX system using LDPC coding and MIMO system under Rayleigh channel. In: Proceedings of IEEE International Conference on International conference on Communication and Signal Processing, India. https://doi.org/10.1109/iccsp.2013.6577107
3GPP TS 36.21 I V8, 5, 0 (2008) Evolved universal terrestrial radio access (E-UTRA), Physical Channels and Modulation (Release 8)
Ketonen J, Juntti M, Cavallaro JR (2010) Performance complexity comparison of receivers for a LTE MIMO-OFDM system. IEEE Trans Signal Process 58(6):3360–3372
Shubhi I, Sanada Y (2014) Performance of turbo codes in overloaded MIMO-OFDM systems using joint decoding. In: Proceedings of IEEE 25th international symposium on personal, indoor and mobile radio communications. https://doi.org/10.1109/PIMRC.2014.7136195
Long Y, Xu W, Jian L (2011) An improved rate matching algorithm for 3GPP LTE turbo code. In: Proceedings of IEEE 3rd International Conference on Communication and Mobile Computing, pp 345–348. https://doi.org/10.1109/CMC.2011.93
C. Wong, H. Chang, “Reconfigurable turbo decoder with parallel architecture for 3GPP LTE system”, IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 57, no. 7, 2010
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Banerjee, S., Chattopadhyay, S. Superposition modulation–based new structure of four-dimensional turbo code (4D-TC) using modified interleaver and its application in WiMAX & LTE systems. Pers Ubiquit Comput 23, 943–959 (2019). https://doi.org/10.1007/s00779-019-01295-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00779-019-01295-0