Cyclic Division Algebras: A Tool for Space-Time Coding

Oggier, Frédérique; Belfiore, Jean-Claude; Viterbo, Emanuele

doi:10.1561/0100000016

Cited by 65 publications

(89 citation statements)

References 50 publications

(109 reference statements)

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“…For more detail examples, the readers are referred to [7]. Furthermore, in [7], it has also been proved that the space-time codes constructed from cyclic division algebra [16], including the wellknown Golden code, are also not delay tolerant.…”

Section: Delay Tolerance Of Space-time Codesmentioning

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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Section: Delay Tolerance Of Space-time Codesmentioning

confidence: 99%

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

Ahmed

Cances²,

Meghdadi³

2012

J Wireless Com Network

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“…The strategy described above consists here of multiplying the received signal at the th relay by the matrix , where is given by (3). Note that in the case of transmit and receive antennas, the algebra structure we are considering is too heavy for our purpose, since the same coding strategy can be obtained more easily as follows [14].…”

Section: E Single Antenna Casementioning

confidence: 99%

“…The interested reader may refer to the original papers [17] and [12] or to a self-contained tutorial [3] for more details. We start by recalling definitions related to number fields, before introducing the definition of cyclic algebra.…”

Section: A Introducing Division Algebrasmentioning

confidence: 99%

An Algebraic Coding Scheme for Wireless Relay Networks With Multiple-Antenna Nodes

Oggier

Hassibi

2008

IEEE Trans. Signal Process.

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Abstract-We consider the problem of coding over a half-duplex wireless relay network where both the transmitter and the receiver have respectively several transmit and receive antennas, whereas each relay is a small device with only a single antenna. Since, in this scenario, requiring the relays to decode results in severe rate hits, we propose a full rate strategy where the relays do a simple operation before forwarding the signal, based on the idea of distributed space-time coding. Our scheme relies on division algebras, an algebraic object which allows the design of fully diverse matrices. The code construction is applicable to systems with any number of transmit/receive antennas and relays, and has better performance than random code constructions, with much less encoding complexity. Finally, the robustness of the proposed distributed space-time codes to node failures is considered.

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“…A dynamic network with a varying number of nodes, out of which a fixed number of n nodes are storing data and the rest are inactive (blank) or equivalently the smallest error probability, that can possibly be achieved by any space-time code. A general construction of MIMO-MAC DMT optimal space-time codes was proposed in [26] for any triple (n t , n r , K) and multiplexing gain r. These MIMO-MAC codes are constructed from cyclic division algebras [23,29] and have a lineardispersion form [30]. Therefore, they can be decoded in the maximal-likelihood (ML) sense by a sphere decoder [31].…”

Section: Introductionmentioning

confidence: 99%

“…By an algebraic lattice we refer to one constructed from a number field extension or a division algebra, see e.g. [29]. 8 It is unfortunate that measuring the exact complexity exponents for these schemes is extremely complicated, and we are unable to complete the task in this paper.…”

mentioning

confidence: 99%

Efficiently sphere-decodable physical layer transmission schemes for wireless storage networks

Barreal

Karpuk

et al. 2016

EURASIP J. Adv. Signal Process.

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Three transmission schemes over a new type of multiple-access channel (MAC) model with inter-source communication links are proposed and investigated in this paper. This new channel model is well motivated by, e.g., wireless distributed storage networks, where communication to repair a lost node takes place from helper nodes to a repairing node over a wireless channel. Since in many wireless networks nodes can come and go in an arbitrary manner, there must be an inherent capability of inter-node communication between every pair of nodes. Assuming that communication is possible between every pair of helper nodes, the newly proposed schemes are based on various smart time-sharing and relaying strategies. In other words, certain helper nodes will be regarded as relays, thereby converting the conventional uncooperative multiple-access channel to a multiple-access relay channel (MARC). The diversity-multiplexing gain tradeoff (DMT) of the system together with efficient sphere-decodability and low structural complexity in terms of the number of antennas required at each end is used as the main design objectives. While the optimal DMT for the new channel model is fully open, it is shown that the proposed schemes outperform the DMT of the simple time-sharing protocol and, in some cases, even the optimal uncooperative MAC DMT. While using a wireless distributed storage network as a motivating example throughout the paper, the MAC transmission techniques proposed here are completely general and as such applicable to any MAC communication with inter-source communication links.

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Cyclic Division Algebras: A Tool for Space-Time Coding

Cited by 65 publications

References 50 publications

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

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

An Algebraic Coding Scheme for Wireless Relay Networks With Multiple-Antenna Nodes

Efficiently sphere-decodable physical layer transmission schemes for wireless storage networks

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