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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 2, 1064 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
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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} }
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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.