Designs and full-rank STBCs from DFT domain description of cyclic codes

Abstract

Viewing an n length vector over F_q ^m as an mtimesn 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 mtimesn matrix over F_q. It is known that under some conditions, n-length cyclic codes over F_q ^m, (n|q^m-1 and mlesn) have full rank. In this paper, using this result we obtain a design using which we construct full-rank space-time block codes (STBCs) for m transmit antennas over signal sets matched to F_q where q = 2 or q is a prime of the form 4k+1. We also propose a construction of STBCs using n-length cyclic codes over F_q ^m, for r transmit antennas, where rlesn and r|m.