Generalized Silver Codes

• Published in: IEEE transactions on information theory 2011-09, Vol.57 (9), p.6134-6147
• Main Authors: Srinath, K. P., Rajan, B. S.
• Format: Article
• Language: English
• Subjects: Antennas; Anticommuting matrices; Applied sciences; Block codes; Coding theory; Coding, codes; Complexity theory; Data transmission; Encoding; ergodic capacity; Exact sciences and technology; full-rate space-time block codes; information losslessness; Information theory; Information, signal and communications theory; low ML- decoding complexity; MIMO; Mutual information; Radiocommunications; Receiving antennas; Signal and communications theory; Silver; Simulation; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitting antennas
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2162276

For an nt transmit, nr receive antenna system ( nt × nr system), a full-rate space time block code (STBC) transmits at least nmin = min ( nt , nr ) 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 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 nr ≥ nt ) but have a high ML-decoding complexity of the order of M n t n min (for n r