Generalized silver codes

Abstract

For an n_t transmit, n_r receive antenna system (n_t × n_t system), a full-rate space time block code (STBC) transmits at least n_min = min(n_t,n_r) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of M^2.5 for square M-QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of M². Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for n_r ≥ n_t) but have a high ML-decoding complexity of the order of M^n_tn_min (for n_r ≥ n_t, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2^a transmit antennas and any n_r with reduced ML-decoding complexity of the order of M^n_t(^{n_min-3/4)-0.5} is presented. The codes constructed are also information lossless for n_r ≥ n_t, like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes for n_r ≥ n_t. These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML-decoding complexity.