High-rate, Multi-Symbol-Decodable STBCs from Clifford Algebras
<|reference_start|>High-rate, Multi-Symbol-Decodable STBCs from Clifford Algebras: It is well known that Space-Time Block Codes (STBCs) obtained from Orthogonal Designs (ODs) are single-symbol-decodable (SSD) and from Quasi-Orthogonal Designs (QODs) are double-symbol decodable. However, there are SSD codes that are not obtainable from ODs and DSD codes that are not obtainable from QODs. In this paper a method of constructing $g$-symbol decodable ($g$-SD) STBCs using representations of Clifford algebras are presented which when specialized to $g=1,2$ gives SSD and DSD codes respectively. For the number of transmit antennas $2^a$ the rate (in complex symbols per channel use) of the $g$-SD codes presented in this paper is $\frac{a+1-g}{2^{a-g}}$. The maximum rate of the DSD STBCs from QODs reported in the literature is $\frac{a}{2^{a-1}}$ which is smaller than the rate $\frac{a-1}{2^{a-2}}$ of the DSD codes of this paper, for $2^a$ transmit antennas. In particular, the reported DSD codes for 8 and 16 transmit antennas offer rates 1 and 3/4 respectively whereas the known STBCs from QODs offer only 3/4 and 1/2 respectively. The construction of this paper is applicable for any number of transmit antennas.<|reference_end|>
@article{karmakar2007high-rate,,
    title={High-rate, Multi-Symbol-Decodable STBCs from Clifford Algebras},
    author={Sanjay Karmakar and B.Sundar Rajan},
    journal={arXiv preprint arXiv:cs/0702023},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702023},
    primaryClass={cs.IT math.IT}
}