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Spacetime code (STC)[1]

Description

Code designed for wireless transmission of information (via, e.g., radio waves) such that the sender can send multiple times from multiple locations. A spacetime code uses a modulation scheme to encode a message into signals that are sent at different times through different antennas, thereby utilizing both spatial and temporal (i.e., spacetime) degrees of freedom.

Rate

Shannon capacity of various multiple-input multiple-output (MIMO) channels has been determined [2–4].

Notes

See the chapter [5] or Ref. [6] for an introduction to spacetime coding.

Cousins

  • Hayden-Nezami-Salton-Sanders bosonic code— Hayden-Nezami-Salton-Sanders codes have been considered in the context of spacetime replication of quantum data [7,8], while STCs are designed to replicate classical data.
  • Codeword stabilized (CWS) code— CWS codes have been considered in the context of spacetime replication of quantum data [7,8], while STCs are designed to replicate classical data.

Member of code lists

Primary Hierarchy

Classical Domain
Matrix Kingdom
Matrix-based codeECC
Parents
Matrix-based code
Spacetime code (STC)
Children
Spacetime block code (STBC)
Spacetime codes also use spatial and temporal diversity, but do not necessarily use blocks as codewords.

References

[1]
V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high data rate wireless communication: performance criterion and code construction”, IEEE Transactions on Information Theory 44, 744 (1998) DOI
[2]
E. Telatar, “Capacity of Multi‐antenna Gaussian Channels”, European Transactions on Telecommunications 10, 585 (1999) DOI
[3]
G. J. Foschini and M. J. Gans, Wireless Personal Communications 6, 311 (1998) DOI
[4]
A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, “Capacity limits of MIMO channels”, IEEE Journal on Selected Areas in Communications 21, 684 (2003) DOI
[5]
B. Clerckx and C. Oestges, “From Multi-Dimensional Propagation to Multi-Link MIMO Channels”, Mimo Wireless Networks 29 (2013) DOI
[6]
F. Oggier, "Spacetime Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[7]
P. Hayden and A. May, “Summoning information in spacetime, or where and when can a qubit be?”, Journal of Physics A: Mathematical and Theoretical 49, 175304 (2016) arXiv:1210.0913 DOI
[8]
P. Hayden, S. Nezami, G. Salton, and B. C. Sanders, “Spacetime replication of continuous variable quantum information”, New Journal of Physics 18, 083043 (2016) arXiv:1601.02544 DOI
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Zoo Code ID: spacetime

Cite as:
“Spacetime code (STC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spacetime
BibTeX:
@incollection{eczoo_spacetime, title={Spacetime code (STC)}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/spacetime} }
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Permanent link:
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Cite as:

“Spacetime code (STC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spacetime

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/spacetime/spacetime.yml.