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Fast Essentially Maximum Likelihood Decoding of the Golden Code

Fast Essentially Maximum Likelihood Decoding of the Golden Code,10.1109/TIT.2011.2136870,IEEE Transactions on Information Theory,Songsri Sirinaunpiboo

Fast Essentially Maximum Likelihood Decoding of the Golden Code   (Citations: 10)
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The Golden code is a full-rate full-diversity space-time code which has been incorporated in the IEEE 802.16 (WiMAX) standard. The worst case complexity of a tree-based sphere decoder for a square QAM constellation is , where is the size of the underlying QAM constellation; the worst case will dominate average decoding complexity on any channel with a significant line of sight component. In this paper, we present a simple algorithm with quadratic complexity for decoding the Golden code that can be employed by mobile terminals with either one or two receive antennas, that is resilient to near singularity of the channel matrix, and that gives essentially maximum likelihood (ML) performance. Dual use is an advantage, since there will likely be some IEEE 802.16 mobile terminals with one receive antenna and some with two antennas. The key to the quadratic algorithm is a maximization of the likelihood function with respect to one of the pair of signal points conditioned on the other. This choice is made by comparing the determinants of two covariance matrices, and the underlying geometry of the Golden code guarantees that one of these choices is good with high probability.
Journal: IEEE Transactions on Information Theory - TIT , vol. 57, no. 6, pp. 3537-3541, 2011
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    • ...Note that this decoding primitive also applies to space‐time codes that are not assisted by quasi-orthogonality, such as the Golden Code [10] and perfect space‐time codes to give essentially ML performance (see [11]and[12]), wherethe tree search implementations employed in [8] do not simplify...
    • ...Note that this decoding primitive can be applied to certain space‐time codes that are not assisted by quasi-orthogonality, such as the Golden Code and perfect space‐time codes to give essentially ML performance [11], [12], where the tree search employed in [8] does not collapse as above...
    • ...The approachisindependentofimplementationandcanbeextendedto produce suboptimal decoding schemes with essentially ML performance for other space‐time codes such as the Golden Code and perfect space‐time block codes [11], [12]...

    Songsri Sirianunpiboonet al. Fast optimal decoding of multiplexed orthogonal designs by conditional...

    • ...The perception that ML decoding of the golden code has high complexity has had two effects: First, it has motivated a search for suboptimal decoders for the golden code with reduced complexity and near-ML performance [13]- [16]...

    Mohanned O. Sinnokrotet al. Fast maximum-likelihood decoding of the golden code

    • ...2 Recently, an essentially ML-decoding algorithm has been given to decode the Golden code with a complexity of only [11]...

    K. Pavan Srinathet al. Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversi...

    • ...The approach has been applied to the Golden code to obtain essentially ML performance with complexity O(N 2 ) [7]...
    • ...The approach is an extension of the ideas used to derive the fast optimal algorithm for multiplexing orthogonal design developed in [8], and applied to Golden code to obtain a fast essentially ML performance decoder [7]...

    Stephen D. Howardet al. Low complexity essentially maximum likelihood decoding of perfect spac...

    • ...can also be decoded optimally or nearly optimally with quadratic complexity [1], [2]...
    • ...These conditions are not satisfied by the Golden code but decoding performance is still indistinguishable from that of ML decoding (see [2])...

    Kalyana C. Bollapalliet al. Highly parallel decoding of space-time codes on graphics processing un...

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