# 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.

## Notes

## Parent

## Child

- Spacetime block code (STBC) — Spacetime codes also use spatial and temporal diversity, but do not necessarily use blocks as codewords.

## Cousins

- Codeword stabilized (CWS) code — CWS codes have been considered in the context of spacetime replication of quantum data [4][5], while STCs are designed to replicate classical data.
- Homological bosonic code — Homological CV codes have been considered in the context of spacetime replication of quantum data [4][5], while STCs are designed to replicate classical data.

## 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]
- B. Clerckx and C. Oestges, “From Multi-Dimensional Propagation to Multi-Link MIMO Channels”, Mimo Wireless Networks 29 (2013). DOI
- [3]
- W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021). DOI
- [4]
- 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). DOI; 1210.0913
- [5]
- P. Hayden et al., “Spacetime replication of continuous variable quantum information”, New Journal of Physics 18, 083043 (2016). DOI; 1601.02544

## Page edit log

- Victor V. Albert (2022-04-21) — most recent

## Zoo code information

## 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/tree/main/codes/classical/matrices/spacetime.yml.