Generalized Silver Codes

Abstract

For an n t transmit, n r receive antenna system (n t × n r system), a full-rate space time block code (STBC) transmits 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 2 transmit antennas. Its ML-decoding complexity is of the order of M 2.5 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 M 2 . 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 ntnmin (for n r < n t , the punctured Perfect codes are considered). In this paper 1 , 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 nt(nmin− 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-Golden codes for 2 transmit antennas. Simulation results of the symbol error rates for 4 and 8 transmit antennasshow that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML-decoding complexity.

An Enhanced DMT-Optimality Criterion for STBC Schemes for Asymmetric MIMO Systems

“…In Appendix B, it is shown that O l = O ′ l almost surely as SN R → ∞. As a result, in the high SNR scenario, (20) becomes…”

“…There exist several low-ML-decoding complexity LSTBC-schemes that have a code-rate less than n t complex dimensions per channel use and are equipped with the NVD property. Examples of these for asymmetric MIMO systems are rate-n r LSTBCschemes that are based on fast-decodable LSTBCs [15] from cyclic division algebras, LSTBC-schemes from co-ordinate interleaved orthogonal designs [16], and four-group decodable LSTBC-schemes [17]- [20]. For these LSTBC-schemes, the sufficient criterion provided in [4] for DMT-optimality, which requires that LSTBCs have a code-rate of n t complex dimensions per channel use irrespective of the number of receive antennas, is not applicable.…”

“…= SN R 1−r , is DMT-optimal for the 2 × 1 MIMO system. Note 2: The described method of obtaining a rate-n r LSTBC from a rate-n t LSTBC (n r < n t ) is called puncturing [20].…”

A fast decodable full-rate STBC with high coding gain for 4 &#x00D7; 2 MIMO systems

“…The so-called fast decodable STBCs [2], [3], [5]- [7] exploit the orthogonality embedded in the codewords and achieve ML decoding performance at a low decoding complexity. For instance, Biglieri-Hong-Viterbo (BHV) constructed a rate-2 STBC [2] based on the classical Jafarkhani code [1].…”

“…This construction idea was then generalized to rate-2 STBC case [5]. Srinath and Rajan (Srinath-Rajan) proposed a fastdecodable rate-2 STBC [6], [7] based on co-ordinate interleaved orthogonal design (CIOD) [8]. The Srinath-Rajan code possesses high coding gain but needs low decoding complexity due to its orthogonal structure.…”