1,548 research outputs found

    Four-Group Decodable Space-Time Block Codes

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    Two new rate-one full-diversity space-time block codes (STBC) are proposed. They are characterized by the \emph{lowest decoding complexity} among the known rate-one STBC, arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection. The first and the second codes are delay-optimal if the number of transmit antennas is a power of 2 and even, respectively. The exact pair-wise error probability is derived to allow for the performance optimization of the two codes. Compared with existing low-decoding complexity STBC, the two new codes offer several advantages such as higher code rate, lower encoding/decoding delay and complexity, lower peak-to-average power ratio, and better performance.Comment: 1 figure. Accepted for publication in IEEE Trans. on Signal Processin

    Signal Set Design for Full-Diversity Low-Decoding-Complexity Differential Scaled-Unitary STBCs

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    The problem of designing high rate, full diversity noncoherent space-time block codes (STBCs) with low encoding and decoding complexity is addressed. First, the notion of gg-group encodable and gg-group decodable linear STBCs is introduced. Then for a known class of rate-1 linear designs, an explicit construction of fully-diverse signal sets that lead to four-group encodable and four-group decodable differential scaled unitary STBCs for any power of two number of antennas is provided. Previous works on differential STBCs either sacrifice decoding complexity for higher rate or sacrifice rate for lower decoding complexity.Comment: 5 pages, 2 figures. To appear in Proceedings of IEEE ISIT 2007, Nice, Franc

    OFDM based Distributed Space Time Coding for Asynchronous Relay Networks

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    Recently Li and Xia have proposed a transmission scheme for wireless relay networks based on the Alamouti space time code and orthogonal frequency division multiplexing to combat the effect of timing errors at the relay nodes. This transmission scheme is amazingly simple and achieves a diversity order of two for any number of relays. Motivated by its simplicity, this scheme is extended to a more general transmission scheme that can achieve full cooperative diversity for any number of relays. The conditions on the distributed space time block code (DSTBC) structure that admit its application in the proposed transmission scheme are identified and it is pointed out that the recently proposed full diversity four group decodable DSTBCs from precoded co-ordinate interleaved orthogonal designs and extended Clifford algebras satisfy these conditions. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Finally, four group decodable distributed differential space time block codes applicable in this new transmission scheme for power of two number of relays are also provided.Comment: 5 pages, 2 figures, to appear in IEEE International Conference on Communications, Beijing, China, May 19-23, 200

    A Novel Construction of Multi-group Decodable Space-Time Block Codes

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    Complex Orthogonal Design (COD) codes are known to have the lowest detection complexity among Space-Time Block Codes (STBCs). However, the rate of square COD codes decreases exponentially with the number of transmit antennas. The Quasi-Orthogonal Design (QOD) codes emerged to provide a compromise between rate and complexity as they offer higher rates compared to COD codes at the expense of an increase of decoding complexity through partially relaxing the orthogonality conditions. The QOD codes were then generalized with the so called g-symbol and g-group decodable STBCs where the number of orthogonal groups of symbols is no longer restricted to two as in the QOD case. However, the adopted approach for the construction of such codes is based on sufficient but not necessary conditions which may limit the achievable rates for any number of orthogonal groups. In this paper, we limit ourselves to the case of Unitary Weight (UW)-g-group decodable STBCs for 2^a transmit antennas where the weight matrices are required to be single thread matrices with non-zero entries in {1,-1,j,-j} and address the problem of finding the highest achievable rate for any number of orthogonal groups. This special type of weight matrices guarantees full symbol-wise diversity and subsumes a wide range of existing codes in the literature. We show that in this case an exhaustive search can be applied to find the maximum achievable rates for UW-g-group decodable STBCs with g>1. For this purpose, we extend our previously proposed approach for constructing UW-2-group decodable STBCs based on necessary and sufficient conditions to the case of UW-g-group decodable STBCs in a recursive manner.Comment: 12 pages, and 5 tables, accepted for publication in IEEE transactions on communication

    Generalized Silver Codes

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    For an ntn_t transmit, nrn_r receive antenna system (nt×nrn_t \times n_r system), a {\it{full-rate}} space time block code (STBC) transmits nmin=min(nt,nr)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 M2.5M^{2.5} for square MM-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 M2M^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 nrntn_r \geq n_t) but have a high ML-decoding complexity of the order of MntnminM^{n_tn_{min}} (for nr<ntn_r < n_t, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2a2^a transmit antennas and any nrn_r with reduced ML-decoding complexity of the order of Mnt(nmin(3/4))0.5M^{n_t(n_{min}-(3/4))-0.5}, is presented. The codes constructed are also information lossless for nrntn_r \geq n_t, like the Perfect codes and allow higher mutual information than the comparable punctured Perfect codes for nr<ntn_r < n_t. These codes are referred to as the {\it 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 antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML-decoding complexity.Comment: Accepted for publication in the IEEE Transactions on Information Theory. This revised version has 30 pages, 7 figures and Section III has been completely revise

    Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

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    Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.Comment: 16 pages, 7 figures; Minor changes in lemmas and construction

    Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

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    For a family/sequence of STBCs C1,C2,\mathcal{C}_1,\mathcal{C}_2,\dots, with increasing number of transmit antennas NiN_i, with rates RiR_i complex symbols per channel use (cspcu), the asymptotic normalized rate is defined as limiRiNi\lim_{i \to \infty}{\frac{R_i}{N_i}}. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least ML decoding complexity among all known codes for any number of transmit antennas N>1N>1 and rates R>1R>1 cspcu. For a large set of (R,N)\left(R,N\right) pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes (R=NR=N) are asymptotically-optimal and fast-decodable, and for N>5N>5 have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper:(i) For g>1g > 1, we construct gg-group ML-decodable codes with rates greater than one cspcu. These codes are asymptotically-good too. For g>2g>2, these are the first instances of gg-group ML-decodable codes with rates greater than 11 cspcu presented in the literature. (ii) We construct a new class of fast-group-decodable codes for all even number of transmit antennas and rates 1<R5/41 < R \leq 5/4.(iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations.Comment: 16 pages, 3 tables. The title has been changed.The class of asymptotically-good multigroup ML decodable codes has been extended to a broader class of number of antennas. New fast-group-decodable codes and asymptotically-optimal, fast-decodable codes have been include

    Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

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    Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 x 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes. Several explicit constructions are presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October 201
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