# Full-Diversity STBCs for Block-Fading Channels from Cyclic Codes

Sripati, U. and Rajan, Sundar B and Shashidhar, V (2004) Full-Diversity STBCs for Block-Fading Channels from Cyclic Codes. In: GLOBECOM '04. IEEE Global Telecommunications Conference, 29 November-3 December, Dallas,Texas, Vol.1, 566 -570.

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## Abstract

Viewing an n-length vector over $F_{q^m}$ (the finite field of $q^m$ elements) as an ${m}\times{n}$ matrix over $F_q$, by expanding each entry of the vector with respect to a basis of $F_{q^m}$ over $F_q$, the rank weight of the n-length vector over $F_{q^m}$ is the rank of the corresponding ${m}\times{n}$ matrix over $F_q$. Using the appropriate discrete Fourier transform (DFT), it is known that, under some conditions, n-length cyclic codes over $F_{q^m}$, $(n|q^m{-1}\hspace{5 mm}and\hspace{5 mm}{m}\leq{n})$, have full-rank $(=m)$. Using this result, we obtain designs for full-diversity space time block codes (STBCs) suitable for block-fading channels from $n$ length cyclic codes over $F_{q^m}$. These STBCs are suitable for $m$ transmit antennas over signal sets matched to $F_q$, where $q=2$ or $q$ is a prime of the form $4k+1$, $(k=1, 2, ...)$. We also present simulation results which illustrate the performance of a few of these STBCs and show that our codes perform better than the well known codes for block-fading channels.

Item Type: Conference Paper http://ieeexplore.ieee.org/iel5/9481/300... Ã�Â©1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Division of Electrical Sciences > Electrical Communication Engineering 08 Dec 2005 19 Sep 2010 04:21 http://eprints.iisc.ernet.in/id/eprint/4340