Some designs and normalized diversity product upper bounds for lattice-based diagonal and full-rate space-time block codes

  • Authors:

  • Huiyong Liao;Haiquan Wang;Xiang-Gen Xia

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Delaware, Newark, DE;College of Communications Engineering, Hangzhou Dianzi University, Hangzhou, China and Department of Electrical and Computer Engineering, University of Delaware, Newark, DE;Department of Electrical and Computer Engineering, University of Delaware, Newark, DE

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

Quantified Score

Hi-index 754.96

Visualization

Abstract

In this paper, we first present two tight upper bounds for the normalized diversity products (or product distances) of 2 × 2 diagonal space-time block codes from quadratic extensions on Q(i) and Q(ζ6), where i = √-1 and ζ6 = exp(i2π/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 Q(i) and Q(ζ6) for three and four transmit antennas. We also present a nontight upper bound for normalized diversity products of 2 × 2 diagonal space-time block codes with QAM information symbols, i.e., in Z [i], from general 2 × 2 complex-valued generating matrices. We then present an n × n-diagonal space-time code design method directly from 2n real integers based on extended complex lattices (of generating matrix size n × 2n) that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do. We finally use the optimal 2 × 2 diagonal space-time codes from the optimal quadratic extensions to construct two 2 × 2 full-rate space-time block codes and find that both of them have better normalized diversity products than the Golden code does.