Multigroup-Decodable STBCs from Clifford Algebras

Karmakar, Sanjay; Rajan, Sanjeev

doi:10.1109/itw2.2006.323839

Cited by 37 publications

(81 citation statements)

References 8 publications

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“…Definition 5: (Multi-group decodable STBCs) An STBC is said to be g-group decodable [29] if its weight matrices can be separated into g groups…”

Section: Definition 1: (Code Rate)mentioning

confidence: 99%

“…For such STBCs, the minimum self-interference is achieved if the STBCs are g-group decodable, with g as large as possible. At present, the best known rate-1 low complexity multi-group decodable codes are the 4-group decodable codes for any number of transmit antennas [27], [28], [29]. These codes are not full-rate for n r > 1.…”

Section: )mentioning

confidence: 99%

“…in literature [27], [28], [29] are not suitable for extension to higher number of receive antennas, since their design is obtained by iterative methods. In the next section, we propose a new design methodology to obtain the weight matrices of a rate-1, 4-group decodable code by algebraic methods for 2 a transmit antennas.…”

Section: )mentioning

confidence: 99%

“…The speciality of the obtained design is that it is amenable for extension to higher number of receive antennas, resulting in full-rate codes with reduced ML-decoding complexity for any number of receive antennas, unlike the previous constructions [27]- [29] of rate-1, 4-group decodable codes.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Silver Codes

Srinath

Rajan

2011

IEEE Trans. Inform. Theory

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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.

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“…Definition 5: (Multi-group decodable STBCs) An STBC is said to be g-group decodable [29] if its weight matrices can be separated into g groups…”

Section: Definition 1: (Code Rate)mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized Silver Codes

Srinath

Rajan

2011

IEEE Trans. Inform. Theory

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“…• Dense full-diversity STBC [29] • Multi-group decodable STBC [63] For the Toeplitz STBC, we choose L = 9 for which the symbol transmission data rate is R s = L/N = 3/4 symbols pcu. To achieve a fair comparison, the same transmission bit rate is imposed on all the codes such that signals are selected from 256-QAM constellation for Toeplitz STBC and from 64-QAM for the other full-rate STBC.…”

Section: Optimal Toeplitz Stbc Design For Miso System With ML Detmentioning

confidence: 99%

Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

Liu

Zhang

Wong

2008

IEEE Trans. Inform. Theory

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Abstract-In this paper, a general criterion for space time block codes (STBC) to achieve full-diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas (MISO). Particularly, the STBC with Toeplitz structure satisfies this criterion and therefore, enables full-diversity. Further examination of this Toeplitz STBC reveals the following important properties: a) The symbol transmission rate can be made to approach unity. b) Applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a non-vanishing determinant. In addition, if QAM is used as the signalling scheme, then for independent MISO flat fading channels, the Toeplitz codes is proved to approach the optimal diversity-vs-multiplexing tradeoff with a ZF receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when ML detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pair-wise error probability.

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