The Golden Code: A&amp;lt;tex&amp;gt;$2,times,2$&amp;lt;/tex&amp;gt;Full-Rate Space–Time Code With Nonvanishing Determinants

Belfiore, Jean-Claude; Rekaya, Ghaya; Viterbo, Emanuele

doi:10.1109/tit.2005.844069

Cited by 666 publications

(154 citation statements)

References 15 publications

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“…It is interesting to notice that for a wide class of linear dispersion (LD) codes [33,19,13,5,43], the information set U is still given by Z m Q , as in the simple V-BLAST case, although the generator matrix G is generally not proportional to I. For other classes of lattice codes [18], with more involved shaping regions R, the information set U does not take on the simple form of an "hypercube".…”

Section: System Modelmentioning

confidence: 99%

A unified framework for tree search decoding: rediscovering the sequential decoder

Murugan

Gamal

Damen

et al. 2006

IEEE Trans. Inform. Theory

270

119

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We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm decomposes into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. We argue that the minimum mean square error decision feedback (MMSE-DFE) frontend is instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for using lattice reduction methods to reduce complexity, at the expense of a marginal performance loss, and solving under-determined linear systems. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSEFano decoder is established via simulation results and analytical arguments in several MIMO and ISI scenarios.

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Section: System Modelmentioning

confidence: 99%

A unified framework for tree search decoding: rediscovering the sequential decoder

Murugan

Gamal

Damen

et al. 2006

IEEE Trans. Inform. Theory

270

119

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“…First, we compare the BER performance of the proposed LJ-OSTBCs with OSTBCs [1], [3], Golden code [5], and QOSTBC [4], which are some typical codes with full space diversity. The channel fadings are constant within one block and vary independently from one block to another.…”

Section: A Performance Under Block-independently Fading Channelsmentioning

confidence: 99%

“…Later, the rate limitation is overcome by quasi-orthogonal STBCs (QOSTBC) by relaxing the orthogonality and slightly increasing decoding complexity, where rate one is reached for more antennas and full space diversity is achieved by special constellation rotation [4]. On the other hand, the full rate alternatives to orthogonal and quasiorthogonal STBCs namely the Golden codes [5] and Perfect codes [6], [7] are introduced to obtain higher rate and larger coding gain. However, they generally have a prohibitively high decoding complexity as all the symbols need to be decoded jointly.…”

Section: Introductionmentioning

confidence: 99%

Diversity gain of lattice constellation‐based joint orthogonal space‐time block coding

et al. 2015

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It is generally thought that space-time block codes (STBCs) can obtain no more than full space diversity. In this paper, we propose a new construction method of joint orthogonal STBCs based on M dimensional lattice constellations for obtaining space and time diversities simultaneously. By deriving the Chernoff bound of error probability, we prove the exact diversity gain of the proposed code is M times of that in traditional STBCs. This is a valuable scheme as diversity gain is usually the primary factor to determine the ability of anti-fading. Moreover, the maximum-likelihood decoder for the proposed code just requires joint decoding of M real symbols, whose complexity is acceptable as M , usually, needs not to be too big. Numerical results show that the proposed code has remarkable improvement of performance compared with some typical STBCs under the comparable low decoding complexity. Index TermsSpace-time block code, multiple-input multiple-output, diversity gain, Chernoff bound, multi-dimensional lattice constellation.

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“…Figure 6 shows the BER and SER performances for codeword matrix (54) without delay. The results are compared with the result of the well-known golden code [23] and the code proposed in [11]. The associated code parameters of (54) are N t = N r = T = 2.…”

Section: Simulationmentioning

confidence: 99%

“…For delay case, we shifted the first row by one symbol interval as shown in (63). The results are compared with the result of wellknown golden code [23] and the code given in [11]. Figure 8 shows the BER and SER performances for codeword matrix (68) without delay.…”

Section: Simulationmentioning

confidence: 99%

Delay tolerant (delto) distributed TAST codes for cooperative wireless networks

Ahmed

Cances²,

Meghdadi³

2012

J Wireless Com Network

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In a distributed cooperative communication system, as the distances between different relay nodes and the receiving nodes may be different, so the performances of distributed space time codes at receiving nodes may badly be degraded if timing synchronization is not assured. In this article, extending the work of Damen et al. we introduce the design of distributed threaded algebraic space-time (TAST) codes offering resistance to timing delay off-set. We present some new and useful techniques of constructing delay tolerant TAST code for distributed cooperative networks, which, like their brethren codes, are delay tolerant for any delay profile and achieve full diversity for arbitrary number of relays, transmit/receive antennas, and input alphabet size. Our proposed codes with minimum lengths achieve better performances than the existing codes retaining full rate and full diversity with or without use of guard bands. Simulations results confirm our claim of obtaining better performances.

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The Golden Code: A<tex>$2,times,2$</tex>Full-Rate Space–Time Code With Nonvanishing Determinants

Cited by 666 publications

References 15 publications

A unified framework for tree search decoding: rediscovering the sequential decoder

A unified framework for tree search decoding: rediscovering the sequential decoder

Diversity gain of lattice constellation‐based joint orthogonal space‐time block coding

Delay tolerant (delto) distributed TAST codes for cooperative wireless networks

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