Description
Code obtained from a parallel concatenation of two or more convolutional codes with permutations interleaving the individual encodings.
The choice of interleaver is important to the code design [3,4].
Protection
Parallel concatenated turbo codes have typical minimum distance with upper bound \(O(\log(n))\). Truhachev, Lentmacher, and Zignagirov produced a sequence of turbo codes with minimum distance \(\Theta(\log(n))\). [5]. Various bounds on code parameters exist [6,7].
Rate
Turbo codes nearly achieve the Shannon capacity [2].
Decoding
Turbo decoder [2], an instance of BP decoding [8].Maximum A Posteriori (MAP) decoder [9] and a soft output derivative [10]. The use of soft outputs can improve code performance [11].List decoding [12].VLSI intergrated-circuit decoding hardware [13].
Realizations
Recommended by Consultative Committee on Space Data Systems (CCDJS) for telemetry and telecommand [14,15].Several standards related to wireless communication, including W-CDMA, DVB-RCS, TD-SCDMA, 802.16, and CDMA2000 [16].
Notes
See Refs. [16–20] for reviews of turbo codes.See database [21] for explicit codes.Codes have been benchmarked using AFF3CT toolbox [22].
Parents
Cousins
- Quadrature-amplitude modulation (QAM) code — Turbo codes concatenated with QAM codes offer a substantial coding gain [23].
- Quadrature-amplitude modulation (QAM) code — Turbo codes can be concatenated with BPSK codes [24].
References
- [1]
- C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes”, IEEE Transactions on Communications 44, 1261 (1996) DOI
- [2]
- C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1”, Proceedings of ICC ’93 - IEEE International Conference on Communications DOI
- [3]
- D. Divsalar and F. Pollara, “Turbo codes for PCS applications”, Proceedings IEEE International Conference on Communications ICC ’95 DOI
- [4]
- H. R. Sadjadpour et al., “Interleaver design for turbo codes”, IEEE Journal on Selected Areas in Communications 19, 831 (2001) DOI
- [5]
- D. Truhachev et al., “On the minimum distance of turbo codes”, Proceedings IEEE International Symposium on Information Theory, DOI
- [6]
- Hui Jin and R. J. McEliece, “Coding theorems for turbo code ensembles”, IEEE Transactions on Information Theory 48, 1451 (2002) DOI
- [7]
- T. M. Duman and M. Salehi, “New performance bounds for turbo codes”, IEEE Transactions on Communications 46, 717 (1998) DOI
- [8]
- R. J. McEliece, D. J. C. MacKay, and Jung-Fu Cheng, “Turbo decoding as an instance of Pearl’s “belief propagation” algorithm”, IEEE Journal on Selected Areas in Communications 16, 140 (1998) DOI
- [9]
- H. R. Sadjadpour, “<title>Maximum a posteriori decoding algorithms for turbo codes</title>”, SPIE Proceedings (2000) DOI
- [10]
- J. D. Kene and K. D. Kulat, “Soft Output Decoding Algorithm for Turbo Codes Implementation in Mobile Wi-Max Environment”, Procedia Technology 6, 666 (2012) DOI
- [11]
- B. Sklar, “A primer on turbo code concepts”, IEEE Communications Magazine 35, 94 (1997) DOI
- [12]
- K. R. Narayanan and G. L. Stuber, “List decoding of turbo codes”, IEEE Transactions on Communications 46, 754 (1998) DOI
- [13]
- G. Masera et al., “VLSI architectures for turbo codes”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems 7, 369 (1999) DOI
- [14]
- Divsalar, Dariush, and Fabrizio Pollara. "Turbo codes for deep-space communications." The Telecommunications and Data Acquisition Report 29-39 (SEE N95-21532 06-32) (1995).
- [15]
- T. Yamada, “CCSDS Telemetry/Tele-command Standards Restructured as Communications Protocols”, SpaceOps 2002 Conference (2002) DOI
- [16]
- K. Gracie and M.-H. Hamon, “Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications”, Proceedings of the IEEE 95, 1228 (2007) DOI
- [17]
- L. Hanzo, T. H. Liew, and B. L. Yeap, Turbo Coding, Turbo Equalisation and Space‐Time Coding (Wiley, 2002) DOI
- [18]
- B. Vucetic and J. Yuan, Turbo Codes (Springer US, 2000) DOI
- [19]
- C. Heegard and S. B. Wicker, Turbo Coding (Springer US, 1999) DOI
- [20]
- L. Hanzo et al., Turbo Coding, Turbo Equalisation and Space–Time Coding (Wiley, 2011) DOI
- [21]
- Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, Stefan Ruzika, and Norbert Wehn. Database of Channel Codes and ML Simulation Results. www.uni-kl.de/channel-codes, 2022.
- [22]
- A. Cassagne et al., “AFF3CT: A Fast Forward Error Correction Toolbox!”, SoftwareX 10, 100345 (2019) DOI
- [23]
- S. Le Goff, A. Glavieux, and C. Berrou, “Turbo-codes and high spectral efficiency modulation”, Proceedings of ICC/SUPERCOMM’94 - 1994 International Conference on Communications DOI
- [24]
- E. K. Hall and S. G. Wilson, “Design and analysis of turbo codes on Rayleigh fading channels”, IEEE Journal on Selected Areas in Communications 16, 160 (1998) DOI
Page edit log
- Victor V. Albert (2023-05-09) — most recent
Cite as:
“Turbo code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/turbo