Full-diversity STBCs for block-fading channels from cyclic codes

Abstract

Viewing an n-length vector over F_qm (the finite field of q^m elements) as an m × n matrix over F_q, by expanding each entry of the vector with respect to a basis of F_qm over F_q, the rank weight of the n-length vector over F_qm is the rank of the corresponding m × n matrix over F_q. Using appropriate Discrete Fourier Transform (DFT), it is known that under some conditions, n-length cyclic codes over F_qm, (n|q^m−1 and m ≤ n), have full-rank (= m). In this paper, 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_qm. 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.