Some Designs and Normalized Diversity Product Upper Bounds for Lattice-Based Diagonal and Full-Rate Space–Time Block Codes
Huiyong Liao, Haiquan Wang, Xiang‐Gen Xia · IEEE Transactions on Information Theory · 2009
In this paper, we first present two tight upper bounds for the normalized diversity products (or product distances) of2 × 2diagonal space-time block codes from quadratic extensions on\BBQ (i)and\BBQ ( \mmbzeta6), where i=radic{-1}and\mmbzeta6=exp(i2pi/6). Two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products. We present two new diagonal space-time block codes from higher order algebraic extensions on\BBQ (i)and\BBQ ( \mmbzeta6)for three and four transmit antennas. We also present a nontight upper bound for normalized diversity products of2 × 2diagonal space-time block codes with QAM information symbols, i.e., in\BBZ [i], from general2 × 2complex-valued generating matrices. We then present ann×n-diagonal space-time code design method directly from2nreal integers based on extended complex lattices (of generating matrix sizen× 2n) that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do. We finally use the optimal2 × 2diagonal space-time codes from the optimal quadratic extensions to construct two2 × 2full-rate space-time block codes and find that both of them have better normalized diversity products than the Golden code does.