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Register a new userEffects of Some Lattice Reductions on the Success Probability of the Zero-Forcing Decoder
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Added by
Jinming Wen
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Zero-forcing (ZF) decoder is a commonly used approximation solution of the integer least squares problem which arises in communications and many other applications. Numerically simulations have shown that the LLL reduction can usually improve the success probability $P_{ZF}$ of the ZF decoder. In this paper, we first rigorously show that both SQRD and V-BLAST, two commonly used lattice reductions, have no effect on $P_{ZF}$. Then, we show that LLL reduction can improve $P_{ZF}$ when $n=2$, we also analyze how the parameter $delta$ in the LLL reduction affects the enhancement of $P_{ZF}$. Finally, an example is given which shows that the LLL reduction decrease $P_{ZF}$ when $ngeq3$.
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This paper is concerned with detecting an integer parameter vector inside a box from a linear model that is corrupted with a noise vector following the Gaussian distribution. One of the commonly used detectors is the maximum likelihood detector, which is obtained by solving a box-constrained integer least squares problem, that is NP-hard. Two other popular detectors are the box-constrained rounding and Babai detectors due to their high efficiency of implementation. In this paper, we first present formulas for the success probabilities (the probabilities of correct detection) of these three detectors for two different situations: the integer parameter vector is deterministic and is uniformly distributed over the constraint box. Then, we give two simple examples to respectively show that the success probability of the box-constrained rounding detector can be larger than that of the box-constrained Babai detector and the latter can be larger than the success probability of the maximum likelihood detector when the parameter vector is deterministic, and prove that the success probability of the box-constrained rounding detector is always not larger than that of the box-constrained Babai detector when the parameter vector is uniformly distributed over the constraint box. Some relations between the results for the box constrained and ordinary cases are presented, and two bounds on the success probability of the maximum likelihood detector, which can easily be computed, are developed. Finally, simulation results are provided to illustrate our main theoretical findings.
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 $1 times N_t$ 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.
For multiple-input multiple-output (MIMO) spatial-multiplexing transmission, zero-forcing detection (ZF) is appealing because of its low complexity. Our recent MIMO ZF performance analysis for Rician--Rayleigh fading, which is relevant in heterogeneous networks, has yielded for the ZF outage probability and ergodic capacity infinite-series expressions. Because they arose from expanding the confluent hypergeometric function $ {_1! F_1} (cdot, cdot, sigma) $ around 0, they do not converge numerically at realistically-high Rician $ K $-factor values. Therefore, herein, we seek to take advantage of the fact that $ {_1! F_1} (cdot, cdot, sigma) $ satisfies a differential equation, i.e., it is a textit{holonomic} function. Holonomic functions can be computed by the textit{holonomic gradient method} (HGM), i.e., by numerically solving the satisfied differential equation. Thus, we first reveal that the moment generating function (m.g.f.) and probability density function (p.d.f.) of the ZF signal-to-noise ratio (SNR) are holonomic. Then, from the differential equation for $ {_1! F_1} (cdot, cdot, sigma) $, we deduce those satisfied by the SNR m.g.f. and p.d.f., and demonstrate that the HGM helps compute the p.d.f. accurately at practically-relevant values of $ K $. Finally, numerical integration of the SNR p.d.f. produced by HGM yields accurate ZF outage probability and ergodic capacity results.
A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, we propose a method based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis reduction algorithms to obtain the integer coefficients for the IF receiver. We show that the proposed method provides a lower bound on the ergodic rate, and achieves the full receive diversity. Suitability of complex Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm (CLLL) to solve the problem is also investigated. Furthermore, we establish the connection between the proposed IF linear receivers and lattice reduction-aided MIMO detectors (with equivalent complexity), and point out the advantages of the former class of receivers over the latter. For the $2 times 2$ and $4times 4$ MIMO channels, we compare the coded-block error rate and bit error rate of the proposed approach with that of other linear receivers. Simulation results show that the proposed approach outperforms the zero-forcing (ZF) receiver, minimum mean square error (MMSE) receiver, and the lattice reduction-aided MIMO detectors.
For stegoschemes arising from error correcting codes, embedding depends on a decoding map for the corresponding code. As decoding maps are usually not complete, embedding can fail. We propose a method to ensure or increase the probability of embedding success for these stegoschemes. This method is based on puncturing codes. We show how the use of punctured codes may also increase the embedding efficiency of the obtained stegoschemes.
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