Kiran, T. ; Rajan, B. S.
(2005)
*Optimal STBCs from codes over galois rings*
In: 2005 IEEE International Conference on Personal Wireless Communications, 2005. ICPWC 2005, 23-25 Jan. 2005, New Delhi, India.

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Official URL: http://ieeexplore.ieee.org/document/1431315/

Related URL: http://dx.doi.org/10.1109/ICPWC.2005.1431315

## Abstract

A Space-Time Block Code (STBC) CST is a finite collection of nt × l complex matrices. If S is a complex signal set, then CST is said to be completely over S if all the entries of each of the codeword matrices are restricted to S. The transmit diversity gain of such a code is equal to the minimum of the ranks of the difference matrices (X − X0 ), for any X 6 = X0 ∈ CST and the rate is R = log|S| |CST| l complex symbols per channel use, where |CST| denotes the cardinality of CST . For a STBC completely over S achieving transmit diversity gain equal to d, the rate is upper-bounded as R ≤ nt − d + 1. An STBC which achieves equality in this tradeoff is said to be optimal. A Rank-Distance (RD) code CF F is a linear code over a finite field Fq, where each codeword is a nt×l matrix over Fq. RD codes have found applications as STBCs by using suitable rank-preserving maps from Fp to S. In this paper, we generalize these rank-preserving maps, leading to generalized constructions of STBCs from codes over Galois ring GR (p a , k). To be precise, for any given value of d, we construct nt ×l matrices over GR (p a , k) and use a rank-preserving map that yields optimal STBCs with transmit diversity gain equal to d. Galois ring includes the finite field Fp k when a = 1 and the integer ring Zpa when k = 1. Our construction includes as a special case, the earlier construction by Lusina et. al. which is applicable only for RD codes over Fp (p = 4s + 1) and transmit diversity gain d.

Item Type: | Conference or Workshop Item (Paper) |
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Source: | Copyright of this article belongs to Institute of Electrical and Electronics Engineers. |

ID Code: | 111190 |

Deposited On: | 08 Dec 2017 10:34 |

Last Modified: | 08 Dec 2017 10:34 |

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