For an ntβ transmit, nrβ receive antenna system (ntβΓnrβ
system), a {\it{full-rate}} space time block code (STBC) transmits nminβ=min(ntβ,nrβ) complex symbols per channel use. The well known Golden code is an
example of a full-rate, full-diversity STBC for 2 transmit antennas. Its
ML-decoding complexity is of the order of M2.5 for square M-QAM. The
Silver code for 2 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 nrββ₯ntβ) but have a high ML-decoding complexity of the order
of Mntβnminβ (for nrβ<ntβ, the punctured Perfect codes are
considered). In this paper, a scheme to obtain full-rate STBCs for 2a
transmit antennas and any nrβ with reduced ML-decoding complexity of the
order of Mntβ(nminββ(3/4))β0.5, is presented. The codes constructed are
also information lossless for nrββ₯ntβ, like the Perfect codes and allow
higher mutual information than the comparable punctured Perfect codes for nrβ<ntβ. These codes are referred to as the {\it 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-Golden codes for 2 transmit antennas. Simulation results of the
symbol error rates for 4 and 8 transmit antennas show that the generalized
Silver codes match the punctured Perfect codes in error performance while
offering lower ML-decoding complexity.Comment: Accepted for publication in the IEEE Transactions on Information
Theory. This revised version has 30 pages, 7 figures and Section III has been
completely revise