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Reduced and Fixed-Complexity Variants of the LLL Algorithm for Communications

IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第3期61卷 1040-1050页

作者： Ling, Cong Mow, Wai Ho Howgrave-Graham, Nick Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Hong Kong Peoples R China Ab Initio Software Corp Lexington MA 02421 USA

The Lenstra-Lenstra-Lovasz (LLL) algorithm is a popular lattice reduction algorithm in communications. In this paper, variants of the LLL algorithm with either reduced or fixed complexity are proposed and analyzed. Specifically, the use of effective LLL reduction for lattice decoding is presented, where size reduction is only performed for pairs of consecutive basis vectors. Its average complexity (measured by the number of floating-point operations and averaged over i.i.d. standard normal lattice bases) is shown to be O(n(3) logn), where n is the lattice dimension. This average complexity is an order lower than previously thought. To address the issue of variable complexity of the LLL algorithm, two fixed-complexity approximations are proposed. One is fixed-complexity effective LLL, for which the first vector of the basis is proven to be bounded in length;the other is fixed-complexity LLL with deep insertion, which is shown to be closely related to the well known V-BLAST algorithm. Such fixed-complexity structures are much desirable in hardware implementation since they allow straightforward constant-throughput implementation.

关键词： Fixed-complexity implementation lattice coding lattice reduction LLL algorithm multi-input multi-output communications

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Evaluation of Codebook Design Using SCMA Scheme Based on A_(n) and D_(n) lattices

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Intelligent Automation & Soft Computing 2023年第3期35卷 3037-3048页

作者： G.Rajamanickam G.Ravi Department of ECE Knowledge Institute of TechnologySalem637504India Department of ECE Sona College of TechnologySalem636001India

The sparse code multiple access(SCMA)scheme is a Non-Orthogonal Multiple Access(NOMA)type of scheme that is used to handle the uplink com-ponent of mobile communication in the current generation.A need of the 5G mobile network is the ability to handle more *** accommodate this,the SCMA allows each user to deploy a variety of sub-carrier broadcasts,and several consumers may contribute to the same frequency using superposition *** SCMA approach,together with codebook design for each user,is used to improve channel efﬁciency through better management of the available ***-ever,developing a codebook with a greater number of value sets is still another *** enhanced techniques of encoding and decoding for 5G networks,mapping the multidimensional constellations in the SCMA system plays a signif-icant role in improving the system performance and enhancing the overall system *** creation of a codebook utilizing the SCMA approach in con-junction with the lattice theory is suggested in this *** prototype is shaped using a popular lattice,such as A n and D n,as the ***,from the primary lattice constellation,the multidimensional complex mother constellation with the most noticeable variance in power is *** lattice-based cod-ing is generated by combining the codebooks with the mother constellation,and the codes in the matrices are mapped by rotating the constellations in this *** suggested technique,in conjunction with the investigation of novel SCMA codebook sets,provides improved performance in terms of Bit Error Rate(BER)and complexity with regard to Signal to Noise Ratio(SNR).Finally,the bit error rate is reduced for various SNRs during transmission in the channel.

关键词： 5G NOMA SCMA lattice coding codebook design bit error rate

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Decoding of constellations matched to the Rayleigh fading channel

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1998年第1-2期53卷 28-38页

作者： Boutillon, E Urunuela, JM Desmassieux, N Ecole Natl Super Telecommun F-75634 Paris 13 France

It has recently been shown that a new class of d-dimensional non-QAM constellations matched for the Rayleigh fading channel (pi-constellations), allows a d-order diversity without addition of redundancy [6-8]. Combined with traditional coding techniques, pi-constellations are very efficient. However;the decoding algorithm of these constellations is far more complicated than that for QAM-constellations. A sub-optimal algorithm for the decoding of pi-constellations is proposed in this work. An example of application for 4 bit/Hz.s spectral efficiency with a 4-D pi-constellations is given and the VLSI architecture of the decoder is described. The implementation, in a 0.8 mu m standard cell technology, can be achieved with a 72 K gate circuit, with a binary rate of 32 Mbit/s and, from simulation, a binary en-or rate of 10(-3) for a SNR of 14 dB.

关键词： signal set decoding Rayleigh fading N dimensional signal real time lattice coding circuit realization VLSI circuit

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Time-invariant and time-varying multirate filter banks: application to image coding

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ANNALS OF TELECOMMUNICATIONS 1998年第5-6期53卷 192-218页

作者： Guillemot, C Rault, P Onno, P CNET CCETT F-35512 Cesson Sevigne France Inst Natl Rech Informat & Automat F-35042 Rennes France Univ British Columbia Vancouver BC V6T124 Canada Canon Res Ctr F-35517 Cesson Sevigne France

This paper reviews various concepts and solutions of time-invariant and time-varying multirate filter banks. It discusses their performance for image and video coding at low bit rates, and their applicability in the MPEG-4 fra-network. Time-invariant multirate filter banks, and methods of design with different criteria appropriate for signal compression are fil st presented. Several procedures of quantization, namely scalar and lattice vector quantization, with bit allocation optimized in the rate-distortion sense, are used for the encoding of the subband signals. A technique of rate-constrained lattice vector quantization (RC-LVQ), combined with a three components entropy coding, allow together with distortion psychovisual weighting mechanisms to obtain significant visual improvements versus scalar quantization or the zerotree technique. However;time-invariant multirate filter banks, although efficient in terms of compression, are not well suited for content-based functionalities. Content-Dosed features may require the ability to manipulate and thus encode a gir en region in the scene independently of the neighbouring regions, hence the rise of transformations that can be adapted to arbitrary size bounded supports. Also, to increase the compression efficiency, one may want to adapt the transformation to the region characteristics, and thus use transform switching mechanisms, with soft or hard transitions. Three main classes of transformations cart address these problems: shape-adaptive block transforms, transforms relying on signal extensions and transforms relying on time-varying multirate filter banks. These various solutions, with their methods of design, al-e reviewed. Emphasis is put on an extension of the SDF (symmetric delay factorization) technique which opens new perspectives in the design of time-bounded and time-varying filter banks. ii region-adapted rate-distortion quantization algorithm has been used in the evaluation of the transformations compressio

关键词： image coding standardization audiovisual service digital filter multichannel circuit low rate block quantization invariance time variation wavelet expansion lattice coding

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Optimal Rate-Limited Secret Key Generation From Gaussian Sources Using lattices

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第8期69卷 4944-4960页

作者： Luzzi, Laura Ling, Cong Bloch, Matthieu R. CY Cergy Paris Univ ENSEA CNRS ETISUMR 8051 F-95014 Cergy Pontoise France Imperial Coll London Dept Elect & Elect Engn London SW7 2AZ England Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

We propose a lattice-based scheme for secret key generation from Gaussian sources in the presence of an eaves-dropper, and show that it achieves the strong secret key capacity in the case of degraded source models, as well as the optimal secret key / public communication rate trade-off. The key ingredients of our scheme are the use of the modulo lattice operation to extract the channel intrinsic randomness, based on the notion of flatness factor, together with a randomized lattice quantization technique to quantize the continuous source. Compared to previous works, we introduce two new notions of flatness factor based on L-1 distance and KL divergence, respectively, which might be of independent interest. We prove the existence of secrecy-good lattices under L-1 distance and KL divergence, whose L-1 and KL flatness factors vanish for volume-to- noise ratios up to 2pe. This improves upon the volume-to- noise ratio threshold 2p of the L8 flatness factor.

关键词： Secret key generation strong secrecy lattice coding flatness factor

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Almost Universal Codes for MIMO Wiretap Channels

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IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第11期64卷 7218-7241页

作者： Luzzi, Laura Vehkalahti, Roope Ling, Cong Univ Cergy Pontoise Univ Paris Seine CNRS ENSEAETISUMR 8051 F-95014 Cergy Pontoise France Univ Turku Dept Math & Stat FI-20014 Turku Finland Aalto Univ Dept Commun & Networking FI-02150 Espoo Finland Imperial Coll London Dept Elect & Elect Engn London SW7 2AZ England

Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information-theoretically secure codes over such channels remains an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel to fading and MIMO wiretap channels, and establish a simple design criterion where the normalized product distance/minimum determinant of the lattice and its dual should be maximized simultaneously. Moreover, we propose concrete lattice codes satisfying this design criterion, which are built from algebraic number fields with constant root discriminant in the single-antenna case, and from division algebras centered at such number fields in the multiple-antenna case. The proposed lattice codes achieve strong secrecy and semantic security for all rates R < C-b - C-e - kappa, where C-b and C-e are Bob and Eve's channel capacities, respectively, and kappa is an explicit constant gap. Furthermore, these codes are almost universal in the sense that a fixed code is good for secrecy for a wide range of fading models. Finally, we consider a compound wiretap model with a more restricted uncertainty set, and show that rates R < (C) over bar (b) - (C) over bar (e) - kappa are achievable, where (C) over bar (b) is a lower bound for Bob's capacity and (C) over bar (e) is an upper bound for Eve's capacity for all the channels in the set.

关键词： Algebraic number theory division algebras fading wiretap channel information theoretic security lattice coding MIMO wiretap channel statistical CSIT

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Non-Linear lattice Precoding for Multiuser Cellular Two-Way Relay Channels

Non-Linear Lattice Precoding for Multiuser Cellular Two-Way ...

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IEEE Global Communications Conference (GLOBECOM)

作者： Fang, Zhaoxi Yuan, Xiaojun Wang, Xin Zhejiang Wanli Univ Dept Commun Engn Ningbo Peoples R China ShanghaiTech Univ Sch Info Sci & Tech Shanghai Peoples R China Fudan Univ Dept Commun Sci & Engn Key Lab EMW Informat MoE Shanghai 200433 Peoples R China

ISBN: (纸本)9781479935123

This paper considers transceiver design for the cellular two-way relay channel (cTWRC), where a multi-antenna base station (BS) exchanges information with multiple single-antenna mobile stations via a multi-antenna relay station. We propose a novel network coding scheme to approach the sum capacity of the cTWRC. Specifically, a new non-linear lattice-based precoding technique is proposed at the BS to pre-compensate the inter-stream interference, in order to allow efficient interference-free lattice decoding at the relay. We derive sufficient conditions for the proposed scheme to asymptotically achieve the sum capacity of the cTWRC in the high signal-to-noise ratio (SNR) regime. Numerical results show that the proposed scheme outperforms the existing schemes and is able to asymptotically achieve the cut-set bound of the cellular relay networks.

关键词： Multiuser two-way relaying lattice coding dirty paper coding non-linear precoding

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The Degrees of Freedom of Compute-and-Forward

The Degrees of Freedom of Compute-and-Forward

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IEEE International Symposium on Information Theory (ISIT)

作者： Niesen, Urs Whiting, Phil Alcatel Lucent Bell Labs Murray Hill NJ 07974 USA

ISBN: (纸本)9781457705953

We analyze the asymptotic behavior of compute-and-forward relay networks in the regime of high signal-to-noise ratios. We consider a section of such a network consisting of K transmitters and K relays. The aim of the relays is to reliably decode an invertible function of the messages sent by the transmitters. An upper bound on the capacity of this system can be obtained by allowing full cooperation among the transmitters and among the relays, transforming the network into a K X K multiple-input multiple-output (MIMO) channel. The number of degrees of freedom of compute-and-forward is hence at most K. In this paper, we analyze the degrees of freedom achieved by the lattice coding implementation of compute-and-forward proposed recently by Nazer and Gastpar. We show that this lattice implementation achieves at most 2/(1 + 1/K) <= 2 degrees of freedom, thus exhibiting a very different asymptotic behavior than the MIMO upper bound. This raises the question if this gap of the lattice implementation to the MIMO upper bound is inherent to compute-and-forward in general. We answer this question to the negative by proposing a novel compute-and-forward implementation achieving K degrees of freedom.

关键词： K relays K transmitters lattices MIMO MIMO channel MIMO communication MIMO upper bound Noise Receivers Relays Transmitters Upper bound channel capacity channel coding compute-and-forward relay networks decoding degrees of freedom lattice coding multiple-input multiple-output channel network coding radio networks signal-to-noise ratio wireless relay network

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Optical Interference Alignment for an Indoor Visible Light Communication X-Channel

Optical Interference Alignment for an Indoor Visible Light C...

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3rd IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Zhang, Xiaoke Gao, Qian Xu, Zhengyuan Chinese Acad Sci Univ Sci & Technol China Sch Informat Sci & Technol Key Lab Wireless Opt Commun Hefei Peoples R China

ISBN: (纸本)9781479975914

In visible light communication (VLC) networks, signals from densely deployed light sources strongly interfere with each other. Proper interference management is expected to improve the VLC system performance. In this article, we propose an optical interference alignment (OIA) approach to minimize mutual interference, where the conventional decodingas-noise scheme is not applicable. A concrete algorithm is provided under lighting constraints with guaranteed decoding error probability. Numerical results demonstrate the significant performance gain offered by this scheme.

关键词： VLC optical interference alignment lighting constraints lattice coding

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An optimal strategy for digital signal parallel processing

An optimal strategy for digital signal parallel processing

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5th International Symposium on Instrumentation and Control Technology

作者： Qian, ZX Qian, LZ Tang, L Dai, YW New Star Res Inst Appl Tech Hefei 230031 Peoples R China

ISBN: (纸本)0819451371

This paper studies the parallel processing algorithms of digital signal linear prediction, especially in speech signals and image signals. An autoregressive digital signal vector series with stable covariance can be obtained by grouping adjacent samples of signal source series and a strategy for vector predictive coding with highly parallel processing ability can be achieved by applying the principle of orthogonal projection in Hilbert space. Then an adaptive parallel processing algorithms for digital signal linear prediction can be given. Compared with traditional lattice methods, the algorithms have an obvious progress in the computation complexity and storage. Finally its performance is tested by computer simulation.

关键词： lattice coding linear prediction parallel processing adaptive algorithm

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