An algebraic MIDO-MISO code construction

Oggier, Frédérique; Hollanti, Camilla; Vehkalahti, Roope

doi:10.1109/spcom.2010.5560533

Cited by 20 publications

(24 citation statements)

References 15 publications

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“…We also present empirical results for an N r × 4 channel. Figure 3 depicts the guaranteed efficiency at 1% for several precoding and receiver topologies, where the algebraic codes considered are orthogonal space-time block precoding (rate 3/4), the perfect code [3], the latter punctured to rate 3, and also the MIDO (rate 2) code [13].…”

Section: ) Comparison Of Bounds and Empirical Resultsmentioning

confidence: 99%

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Explicit lower bounds on the outage probability of integer forcing over N<inf>r</inf> × 2 channels

Domanovitz

Erez

2017

2017 IEEE Information Theory Workshop (ITW)

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The performance of integer-forcing equalization for communication over the compound multiple-input multipleoutput channel is investigated. An upper bound on the resulting outage probability as a function of the gap to capacity has been derived previously, assuming a random precoding matrix drawn from the circular unitary ensemble is applied prior to transmission. In the present work a simple and explicit lower bound on the worst-case outage probability is derived for the case of a system with two transmit antennas and two or more receive antennas, leveraging the properties of the Jacobi ensemble. The derived lower bound is also extended to random space-time precoding, and may serve as a useful benchmark for assessing the relative merits of various algebraic space-time precoding schemes. We further show that the lower bound may be adapted to the case of a 1 × Nt system. As an application of this, we derive closed-form bounds for the symmetric-rate capacity of the Rayleigh fading multiple-access channel where all terminals are equipped with a single antenna. Lastly, we demonstrate that the integer-forcing equalization coupled with distributed space-time coding is able to approach these bounds. 10 When using an ML receiver, this space-time code is known to achieve the DMT for multiplexing rates r ≤ 1 5 . As detailed in [16], whether this code achieves the optimal MAC-DMT also when r > 1 5 remains an open question.

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Section: ) Comparison Of Bounds and Empirical Resultsmentioning

confidence: 99%

“…Note that (45) is a special case of (13). While in general applying a CUE precoding transformation P c implies joint processing at the encoders, which is precluded in a MAC setting, in an i.i.d.…”

Section: Application: Closed-form Bounds For the Symmetric-rate Cmentioning

confidence: 99%

Explicit lower bounds on the outage probability of integer forcing over N<inf>r</inf> × 2 channels

Domanovitz

Erez

2017

2017 IEEE Information Theory Workshop (ITW)

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“…It is clear that γ M = −ω / ∈ Q(θ). The rate-2 STBC (unnormalized with respect to SNR) for 12 transmit antennas is given by (17) at the top of the next page with …”

Section: ) Minimum Determinantmentioning

confidence: 99%

Fast-Decodable MIDO Codes With Large Coding Gain

Srinath¹,

Rajan

2014

IEEE Trans. Inform. Theory

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Abstract-In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of 2 complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input, double output (MIDO) systems. Using this method, rate-2 STBCs for 4×2, 6×2, 8×2 and 12×2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the Srinath-Rajan code [R. Vehkalahti, C. Hollanti, and F. Oggier, "Fast-Decodable Asymmetric Space-Time Codes from Division Algebras," IEEE Trans. Inf. Theory, Apr. 2012] for the 4×2 system, which has the lowest ML-decoding complexity among known rate-2 STBCs for the 4 × 2 MIDO system with a large coding gain for 4-/16-QAM, has the same algebraic structure as the STBC constructed in this paper for the 4 × 2 system. This also settles in positive a previous conjecture that the STBC-scheme that is based on the SrinathRajan code has the NVD property and hence is DMT-optimal for the 4 × 2 system.

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“…Precisely, a CRT array is constructed by two coprime lattices generated from two quadratic integers respectively in the same field. According to the generalized CRT stated in [6], the difference vectors of two coprime lattices enjoy a quadratic surge of DOF, which allows the identification of more sources than the number of sensors. The coprimality of lattices is guaranteed by the coprimality of their corresponding quadratic integers [5,Theroem 1].…”

Section: Introductionmentioning

confidence: 99%

Coprime Sensing via Chinese Remaindering Over Quadratic Fields—Part II: Generalizations and Applications

Liu

Ling

2019

IEEE Trans. Signal Process.

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The practical application of a new class of coprime arrays based on the Chinese remainder theorem (CRT) over quadratic fields is presented in this paper. The proposed CRT arrays are constructed by ideal lattices embedded from coprime quadratic integers with B1 and B2 being their matrix representations respectively, whereby the degrees of freedom (DOF)The geometrical constructions and theoretical foundations were discussed in the accompanying paper in great detail, while this paper focuses on aspects of the application of the proposed arrays in two-dimensional (2D) remote sensing. A generalization of CRT arrays based on two or more pairwise coprime ideal lattices is proposed with closed-form expressions on sensor locations, the total number of sensors and the achievable DOF. The issues pertaining to the coprimality of any two quadratic integers are also addressed to explore all possible ideal lattices. Exploiting the symmetry of lattices, sensor reduction methods are discussed with the coarray remaining intact for economic maximization. In order to extend conventional angle estimation techniques based on uniformly distributed arrays to the method that can exploit any coarray configurations based on lattices, this paper introduces a hexagon-to-rectangular transformation to 2D spatial smoothing, providing the possibility of finding more compact sensor arrays. Examples are provided to verify the feasibility of the proposed methods.

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An algebraic MIDO-MISO code construction

Cited by 20 publications

References 15 publications

Explicit lower bounds on the outage probability of integer forcing over N<inf>r</inf> × 2 channels

Explicit lower bounds on the outage probability of integer forcing over N<inf>r</inf> × 2 channels

Fast-Decodable MIDO Codes With Large Coding Gain

Coprime Sensing via Chinese Remaindering Over Quadratic Fields—Part II: Generalizations and Applications

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