Orthogonal Spacetime Block Code (OSTBC)[1]

Description

The codewords are \(T\times n\) matrices as defined for spacetime codes, with the additional condition that columns of the coding matrix are orthogonal. The parameter \(n\) is the number of channels, and \(T\) is the number of time slots.

Protection

If the matrix \(C-C'\), where \(C\) and \(C'\) are distinct codewords, has minimum rank \(b\), the code has diversity order \(bn_R\) (see Ref. [2], Sec. 28.2.1), where \(n_R\) is the number of receivers. The maximum possible diversity order is \(nn_R\).

Rate

The greatest rate which can be achieved is \(\frac{n_0+1}{2n_0}\), where either \(n=2n_0\) or \(n=2n_0-1\) [3].

Decoding

Maximum-likelihood decoding can be achieved with only linear processing [4].

Parent

Child

Zoo code information

Internal code ID: orth_spacetime_block

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: orth_spacetime_block

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

References

[1]
S. M. Alamouti, “A simple transmit diversity technique for wireless communications”, IEEE Journal on Selected Areas in Communications 16, 1451 (1998). DOI
[2]
W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021). DOI
[3]
Xue-Bin Liang, “Orthogonal designs with maximal rates”, IEEE Transactions on Information Theory 49, 2468 (2003). DOI
[4]
V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block coding for wireless communications: performance results”, IEEE Journal on Selected Areas in Communications 17, 451 (1999). DOI

Cite as:

“Orthogonal Spacetime Block Code (OSTBC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/orth_spacetime_block

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/matrices/orth_spacetime_block.yml.