On the algebraic structure of the Silver code: A 2 &amp;#x00D7; 2 perfect space-time block code

Hollanti, Camilla; Lahtonen, Jyrki; Ranto, Kalle; Vehkalahti, Roope; Viterbo, Emanuele

doi:10.1109/itw.2008.4578628

Cited by 36 publications

(22 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The latter subsection, for its part, describes a K-user code taking advantage of the Silver algebra [21]. The Silver code [22] has performance only slightly worse than that of the Golden or Golden+ code, but it is simpler to decode as it can be constructed with the aid of two Alamouti blocks.…”

Section: For Any Subset Of Usersmentioning

confidence: 99%

See 1 more Smart Citation

An algebraic tool for obtaining conditional non-vanishing determinants

Hollanti

Vehkalahti

2009

2009 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

An algebraic tool from the theory of central simple algebras is proposed to obtain families of complex matrices satisfying the conditional non-vanishing determinant (CNVD) property. Such property is of great use in e.g. the design of multiuser space-time (ST) codes, in which context it is not always crucial for the transmission matrix to be invertible. On the other hand, whenever it is invertible, it is important that it has a non-vanishing determinant. Also any submatrix of any subset of users multiplied with its transpose conjugate should preferably have a non-vanishing determinant, provided it is non-zero. In recent submissions by Lu et al. it has been shown that, with suitable multiplexing, such property yields a construction of space-time codes that achieve the optimal diversity-multiplexing tradeoff (DMT) of the multipleinput multiple-output (MIMO) multiple access channel (MAC) and outperform the previously known ST codes.

show abstract

Section: For Any Subset Of Usersmentioning

confidence: 99%

“…In [21] it was shown that the Silver code is a subset in the cyclic division algebra D = (Q( √ −7, i)/Q( √ −7), σ , γ = −1), where σ (i) = −i and σ ( √ 7) = − √ 7. Let now Λ ⊆ D be an order, and x i j ∈ Λ, i, j ∈ {1, ..., K}.…”

Section: B a K-user Code From The Silver Algebramentioning

confidence: 99%

An algebraic tool for obtaining conditional non-vanishing determinants

Hollanti

Vehkalahti

2009

2009 IEEE International Symposium on Information Theory

View full text Add to dashboard Cite

show abstract

“…II for a formal definition). For 2 transmit antennas, the Silver code, named so in [6], was first mentioned in [7] and independently presented in [8] along with a study of its low MLdecoding complexity property. It is a full-rate code with full-diversity and an ML-decoding complexity of the order of M 2 for square M -QAM.…”

Section: Introductionmentioning

confidence: 99%

“…It is a full-rate code with full-diversity and an ML-decoding complexity of the order of M 2 for square M -QAM. Its algebraic properties have been studied in [6] and [9] and a fixed point fast decoding scheme has been given in [10]. For 4 transmit antennas, Biglieri et.…”

Section: Introductionmentioning

confidence: 99%

Generalized Silver Codes

Srinath

Rajan

2011

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

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.

show abstract

“…In [8], [9], it was shown that the Golden Code [10], which is a perfect code [11], is fast-decodable and hence has lower ML decoding complexity than was previously known. The Silver code [12], [13], [14], which is a perfect code for 2 978-1-61284-233-2/11/$26.00 ©2011 IEEE antennas, is also fast-decodable. In [8], rate 2 codes using designs for 2 and 4 antennas with the largest known coding gain were constructed.…”

Section: Introductionmentioning

confidence: 99%

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Natarajan¹,

Rajan²

2011

2011 IEEE International Conference on Communications (ICC)

View full text Add to dashboard Cite

Recently in [1], a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field F 4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over F 4 for number of transmit antennas N = 2 m , m > 1, and rates R > 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N, R) pairs. The new full-rate codes of this paper (R = N ) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over F 4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations.

show abstract

On the algebraic structure of the Silver code: A 2 × 2 perfect space-time block code

Cited by 36 publications

References 11 publications

An algebraic tool for obtaining conditional non-vanishing determinants

An algebraic tool for obtaining conditional non-vanishing determinants

Generalized Silver Codes

Fast-Group-Decodable STBCs via Codes over GF(4): Further Results

Contact Info

Product

Resources

About