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

Viewing an n-length vector over F(q^m) (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(q^m) over F_q, the rank weight of the n-length vector over F(q^m) is the rank of the corresponding m×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 and m≤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.