Remarks on the criteria of constructing MIMO-MAC DMT optimal codes

Lu, Hsiao-feng; Lahtonen, Jyrki; Vehkalahti, Roope; Hollanti, Camilla

doi:10.1109/itwksps.2010.5503180

Cited by 9 publications

(18 citation statements)

References 9 publications

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“…Using the geometrical argument, we showed that the outage bound in [1] is not limiting for the outage probability as claimed in [6]. Moreover, a new family of split NVD parallel codes to achieve the optimal DMT in [5] for the case of time or frequency selective channels is proposed.…”

Section: Discussionmentioning

confidence: 97%

How to achieve the optimal DMT of selective fading MIMO channels?

Mroueh

Belfiore

2010

2010 IEEE Information Theory Workshop

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In this paper, we extend the non-vanishing determinant (NVD) criterion to the selective fading channel case. A new family of split NVD parallel codes, that satisfies this design criterion, is proposed to achieve the optimal diversity multiplexing tradeoff (DMT) derived by Coronel and Bölcskei, IEEE ISIT, 2007. This result is of significant interest not only in its own right, but also because it settles a long-standing debate in the literature related to the optimal DMT of selective fading channels.

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Section: Discussionmentioning

confidence: 97%

How to achieve the optimal DMT of selective fading MIMO channels?

Mroueh

Belfiore

2010

2010 IEEE Information Theory Workshop

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“…Some progress in these questions has been made in [4], [3], [2], and it is easy to believe that a condition expressed in terms of the decay function is also out there [4]. In this note we state some interesting results from [5] about the available decay functions of all MU-MIMO lattice codes in general. Based on them, and as the main contribution of this paper, we study in particular the decay function of the code proposed by Badr & Belfiore (BB-code, in short).…”

Section: Background and The Decay Functionmentioning

confidence: 94%

On the decay of the determinants of multiuser MIMO lattice codes

Lahtonen

Vehkalahti

et al. 2010

IEEE Information Theory Workshop 2010 (ITW 2010)

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Abstract-In a recent work, Coronel et al. initiated the study of the relation between the diversity-multiplexing tradeoff (DMT) performance of a multiuser multiple-input multiple-output (MU-MIMO) lattice code and the rate of the decay of the determinants of the code matrix as a function of the size of the signal constellation. In this note, we state a simple general upper bound on the decay function and study the promising code proposed by Badr & Belfiore in close detail. We derive a lower bound to its decay function based on a classical theorem due to Liouville. The resulting bound is applicable also to other codes with constructions based on algebraic number theory. Further, we study an example sequence of small determinants within the Badr-Belfiore code and derive a tighter upper bound to its decay function. The upper bound has certain conjectural asymptotic uncertainties, whence we also list the exact bound for several finite data rates. I. BACKGROUND AND THE DECAY FUNCTIONAssume that we are to design a system for U simultaneously transmitting synchronized users, each transmitting with n t transmit antennas and, for simplicity so that we end up with square matrices, over U n t channel uses. We can describe each user's signals as n t × U n t complex matrices. A multiuser MIMO signal is then viewed as a U n t × U n t matrix obtained by using the signals of the individual users as blocks. So each user is occupying n t rows in this overall transmission matrix.Any study of DMT questions calls for a scalable set of finite signal constellations. For the sake of convenience most authors assume that these signal sets of individual users are carved out of a user specific lattice L j ⊂ M nt×Unt , j = 1, . . . , U .When studying DMT questions it is natural to assume that each user is maximally using the degrees of freedom available to him/her. Therefore, the lattices of the individual users should be of full rank n = 2U n 2 t , so that each user's signals consist of integral linear combinations of n user specific basis matrices. A natural scaling parameter is the range of the integer coefficients. We assume that the range is parameterized by a natural number N .

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“…This corresponds to a MIMO MAC space-time code, which are known ( [11], [15]) to perform well and to achieve the socalled diversity-multiplexing gain tradeoff (DMT) [10], when the field is chosen well. With sufficient SNR, the receiver is able to decode the message with very high probability and gets b , c , which he can map back to bit strings b, c = a + b and further reveal a = b + (a + b).…”

Section: Space-time Storage Codes Over Macmentioning

confidence: 99%

“…As the channel quality is imposed by nature, we will concentrate on designing the space-time code as well as possible. To this end, the ST code C ST consisting of a finite number of the matrices (1) should have the following property that we recite from [15].…”

Section: Design Criteria For Space-time Storage Codesmentioning

confidence: 99%

Space-time storage codes for wireless distributed storage systems

Hollanti

Karpuk

Barreal

et al. 2014

2014 4th International Conference on Wireless Communications, Vehicular Technology, Information Theory and Aerospace &Amp; Elec

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Abstract-Distributed storage systems (DSSs) have gained a lot of interest recently, thanks to their robustness and scalability compared to single-device storage. Majority of the related research has exclusively concerned the network layer. At the same time, the number of users of, e.g., peer-to-peer (p2p) and deviceto-device (d2d) networks as well as proximity based services is growing rapidly, and the mobility of users is considered more and more important. This motivates, in contrast to the existing literature, the study of the physical layer functionality of wireless distributed storage systems.In this paper, we take the first step towards protecting the storage repair transmissions from physical layer errors when the transmission takes place over a fading channel. To this end, we introduce the notion of a space-time storage code, drawing together the aspects of network layer and physical layer functionality and resulting in cross-layer robustness. It is also pointed out that existing space-time codes are too complex to be utilized in storage networks when the number of helpers involved is larger than the number of receive antennas at the newcomer or data collector, hence creating a call for less complex transmission protocols.

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Remarks on the criteria of constructing MIMO-MAC DMT optimal codes

Cited by 9 publications

References 9 publications

How to achieve the optimal DMT of selective fading MIMO channels?

How to achieve the optimal DMT of selective fading MIMO channels?

On the decay of the determinants of multiuser MIMO lattice codes

Space-time storage codes for wireless distributed storage systems

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