[Jump to code hierarchy]

Turbo code[1,2]

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 of order \(\Theta(\log(n))\). [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].Autoencoder [14].

Realizations

Recommended by Consultative Committee on Space Data Systems (CCDJS) for telemetry and telecommand [15,16].Several standards related to wireless communication, including W-CDMA, DVB-RCS, TD-SCDMA, 802.16, and CDMA2000 [17].

Notes

See Refs. [17–21] for reviews of turbo codes.See database [22] for explicit codes.Codes have been benchmarked using AFF3CT toolbox [23].

Cousins

Member of code lists

Primary Hierarchy

Classical Domain
Error-correcting code (ECC)
Block code
Convolutional code
Parents
Convolutional code
Parallel concatenated codeECC
Turbo code

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 1, 54 DOI
[4]
H. R. Sadjadpour, N. J. A. Sloane, M. Salehi, and G. Nebe, “Interleaver design for turbo codes”, IEEE Journal on Selected Areas in Communications 19, 831 (2001) DOI
[5]
D. Truhachev, M. Lentmaier, O. Wintzell, and K. Sh. Zigangirov, “On the minimum distance of turbo codes”, Proceedings IEEE International Symposium on Information Theory, 84 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 4045, 73 (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, G. Piccinini, M. R. Roch, and M. Zamboni, “VLSI architectures for turbo codes”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems 7, 369 (1999) DOI
[14]
E. Balevi and J. G. Andrews, “Autoencoder-Based Error Correction Coding for One-Bit Quantization”, (2019) arXiv:1909.12120
[15]
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).
[16]
T. Yamada, “CCSDS Telemetry/Tele-command Standards Restructured as Communications Protocols”, SpaceOps 2002 Conference (2002) DOI
[17]
K. Gracie and M.-H. Hamon, “Turbo and Turbo-Like Codes: Principles and Applications in Telecommunications”, Proceedings of the IEEE 95, 1228 (2007) DOI
[18]
L. Hanzo, T. H. Liew, and B. L. Yeap, Turbo Coding, Turbo Equalisation and Space‐Time Coding (Wiley, 2002) DOI
[19]
B. Vucetic and J. Yuan, Turbo Codes (Springer US, 2000) DOI
[20]
C. Heegard and S. B. Wicker, Turbo Coding (Springer US, 1999) DOI
[21]
L. Hanzo, T. H. Liew, B. L. Yeap, R. Y. S. Tee, and S. X. Ng, Turbo Coding, Turbo Equalisation and Space–Time Coding (Wiley, 2011) DOI
[22]
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.
[23]
A. Cassagne et al., “AFF3CT: A Fast Forward Error Correction Toolbox!”, SoftwareX 10, 100345 (2019) DOI
[24]
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 645 DOI
[25]
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

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: turbo

Cite as:
“Turbo code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/turbo
BibTeX:
@incollection{eczoo_turbo, title={Turbo code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/turbo} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/turbo

Cite as:

“Turbo code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/turbo

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/convolutional/turbo.yml.