Publications (140)71.88 Total impact
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ABSTRACT: The recently discovered family of generalized lowdensity (GLD) lattices brings new mathematical challenges to coding theorists and practitioners. Given the excellent performance of integer GLD lattices in high dimensions and motivated by the simple lattice structure used for fast iterative decoding, this paper is a first attempt to analyze GLD lattices for asymptotically large dimensions. Firstly, we describe nonbinary GLD codes and show their asymptotic goodness in terms of minimum Hamming distance. Secondly, we consider a GLD lattice ensemble built via Construction A from nonbinary GLD codes, and analyze their goodness with respect to Poltyrev limit on the Gaussian channel. Finally, at large dimensions and using a large code alphabet, we prove that infinite GLD lattice constellations attain Poltyrev capacity limit under maximum likelihood decoding.  [Show abstract] [Hide abstract]
ABSTRACT: We propose the construction of a new family of lattice sphere packings. Given a smalldimensional lattice, we start by building a first lattice in a large dimension by the direct sum of the small lattice. Then, the coordinates of the first large lattice are permuted to yield a second largedimensional lattice. Finally, our generalized lowdensity (GLD) lattice is the intersection of the first and the second lattice. We restrict our construction in this paper to integer lattices. GLD lattices are the result of mixing classical lattice theory with modern coding theory. They are potential candidates not only for channel coding as coded modulations, but also for physicallayer network coding and for secure digital communications.  [Show abstract] [Hide abstract]
ABSTRACT: The computeandforward (CoF) is a relaying protocol, which uses algebraic structured codes to harness the interference and remove the noise in wireless networks. We propose the use of phase precoders at the transmitters of a network, where relays apply CoF strategy. Firstly, we define the {\em phase precoded computation rate} and show that it is greater than the original computation rate of CoF protocol. To maximize the phase precoded computation rate, we need to solve a mixed integer programming problem where the optimum precoders should be obtained at the transmitters and the network equation coefficients have to be computed at the relays. To practically solve this problem, we introduce the phase precoded CoF with limited feedback. This is a quantized precoding system, where the relay jointly computes both a quasioptimal precoder from a finite codebook and the corresponding network equations. The index of the obtained phase precoder within the codebook is then fedback to the transmitters. Secondly, we show that the proposed precoding scheme increases the degreesoffreedom (DoF) of CoF protocol. This overcomes the limitations on the DoF of the CoF protocol, recently presented by Niesen and Whiting. Using tools from Diophantine approximation and algebraic geometry, we prove the existence of a phase precoder that achieves the maximum DoF when the number of transmitters tends to infinity. Finally, we conduct computer simulations to verify the effectiveness of the proposed phase precoding technique. We further give a new lowcomplexity method for finding network equations. The gain in computation rate and the higher DoF expected from theoretical results are confirmed by computer simulations with lattice codes. 
Dataset: Liu GLOBECOM08.pdf

Conference Paper: An asymptotic approximation of the ISI channel capacity
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ABSTRACT: An asymptotic method to calculate the information rate of an ISI channel is presented in this work. The method is based on an integral representation of the mutual information, which is then calculated by using a saddlepoint approximation along with an asymptotic expansion stemming from the HubbardStratonovich transform. This asymptotic result is evaluated repeatedly to generate a large number of samples required for the MonteCarlo approximation of the final result. The proposed method has the advantage of being manageable even when the channel memory becomes very large since the complexity grows with polynomial order in the memory length.  [Show abstract] [Hide abstract]
ABSTRACT: In this work, we propose phase precoding for the computeandforward (CoF) protocol. We derive the phase precoded computation rate and show that it is greater than the original computation rate of CoF protocol without precoder. To maximize the phase precoded computation rate, we need to 'jointly' find the optimum phase precoding matrix and the corresponding network equation coefficients. This is a mixed integer programming problem where the optimum precoders should be obtained at the transmitters and the network equation coefficients have to be computed at the relays. To solve this problem, we introduce phase precoded CoF with partial feedback. It is a quantized precoding system where the relay jointly computes both a quasioptimal precoder from a finite codebook and the corresponding network equations. The index of the obtained phase precoder within the codebook will then be fedback to the transmitters. A "deep hole phase precoder" is presented as an example of such a scheme. We further simulate our scheme with a lattice code carved out of the Gosset lattice and show that significant coding gains can be obtained in terms of equation error performance. 
Conference Paper: Polarization of quasistatic fading channels
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ABSTRACT: This work investigates polar coding for blockfading channels. We show that polarization does occur at infinity for three types of channel multiplexers. Nevertheless, the polarization process is not unique, as it is shaped by the choice of the multiplexer. The fadingplane approach is used to study the outage behavior of polar coding at a fixed transmission rate. Two types of multiplexers are shown to provide full diversity at finite and infinite code length.  [Show abstract] [Hide abstract]
ABSTRACT: We address the problem of transmission of information over the AWGN channel using lattices. In particular, we will deal with previously introduced LDA lattices which are obtained by Construction A from LDPC codes over the finite field Fp. We will show how to build a particular ensemble of LDA lattices related to bipartite graphs with good expansion properties. We investigate the quality of this family under lattice decoding and show that a random member in it can be reliably decoded for any value of the channel noise variance up to Poltyrev limit. Values of p and the parameters for which optimal performance is guaranteed under lattice decoding are in accordance with the optimal parameters found experimentally under iterative decoding. 
Conference Paper: New results on lowdensity integer lattices
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ABSTRACT: A new family of integer lattices built from Construction A and nonbinary lowdensity paritycheck (LDPC) codes has been proposed by the authors in 2012. Lattices in this family are referred to as LDA lattices. Previous experimental results revealed excellent performance which clearly single out LDA lattices among the strongest candidates for potential applications in digital communications and networks, such as network coding and information theoretic security at the physical layer level. In this paper, we show that replacing random codes by LDPC codes in Construction A does not induce any structural loss. More precisely, our main theorem states that LDA lattices can achieve Poltyrev capacity limit on an additive white Gaussian noise channel. We present here the detailed proof and its consequences on the lattice dimension, the finite field size, and the parameters of the LDPC ensemble. The latter has a row weight that increases logarithmically in the code length. In a more recent work, it is proved that the Poltyrev limit is attained by a different LDA ensemble having a small constant row weight. 
Conference Paper: Lattices Over Eisenstein Integers for ComputeandForward
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ABSTRACT: We consider the use of lattice codes over Eisenstein integers for implementing a computeandforward protocol in wireless networks when channel state information is not available at the transmitter. We prove the existence of a sequence of infinitedimensional nested lattices over Eisenstein integers where the coarse lattice is simultaneously good for quantization and additive white Gaussian noise (AWGN) channel coding and the fine lattice is good for AWGN channel coding. Using this, we show that the information rates achievable with nested lattice codebooks over Eisenstein integers can be higher than those achievable with nested lattices over integers considered by Nazer and Gastpar in [1] for some set of channel realizations. We also propose a practical coding scheme based on the concatenation of a nonbinary low density parity check code with a modulation scheme derived from the ring of Eisenstein integers. 
Conference Paper: Integer LowDensity Lattices based on Construction A
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ABSTRACT: We describe a new family of integer lattices built from construction A and nonbinary LDPC codes. An iterative messagepassing algorithm suitable for decoding in high dimensions is proposed. This family of lattices, referred to as LDA lattices, follows the recent transition of Euclidean codes from their classical theory to their modern approach as announced by the pioneering work of Loeliger (1997), Erez, Litsyn, and Zamir (20042005). Besides their excellent performance near the capacity limit, LDA lattice construction is conceptually simpler than previously proposed lattices based on multiple nested binary codes and LDA decoding is less complex than realvalued message passing. 
Article: Precoding for Word Error Rate Minimization of LDPC Coded Modulation on Block Fading Channels
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ABSTRACT: In wireless communications, the block fading (BF) channel is an important channel model. A key quality indicator in coded transmission is the word error rate (WER), which is the fraction of packets that cannot be decoded correctly at the receiver. We study LowDensity ParityCheck (LDPC) coded modulation with precoding, with the aim to minimize the WER on BF channels without channel state information at the transmitter. In the literature, it was not yet known how to optimize the system parameters for this channel model, mainly due to the fading gain distribution. One of the existing approaches to combining coding and modulation is bitinterleaved coded modulation with iterative decoding (BICMID). This work uses precoding to optimize BICMID with LDPC codes for BF channels, and is a continuation of previous work that used precoding to minimize the outage probability limit. We present the selection of the precoding matrix, the mapping function and the errorcorrecting code yielding a WER that closely approaches this minimum outage probability. Using a geometric approach, the offline system optimization effort for the BF channel is limited to at most B+1 times the effort for Gaussian channels, where B is the number of blocks in the BF channel. 
Conference Paper: Timevarying spaceonly codes
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ABSTRACT: Multiple antennas are used to increase reliability and bit rate for a given bandwidth. For a fixed transmission rate, discrete input alphabets and no channel state information at the transmitter, optimal spacetime codes (STCs) achieving both gains (full rate and full diversity) are well known. However, the complexity of maximum likelihood decoding increases exponentially with the number of space and time dimensions of the STC. Despite praiseworthy efforts to reduce the decoding complexity, optimal STCs are not used in practice in the case of more than two transmit antennas because of complexity reasons. It is generally accepted that reducing the dimension of the STC leads to a reduced diversity order. We show that this is not true for coded communication, assuming the presence of an outer errorcorrecting code with any coding rate. We propose a new class of fullrate fulldiversity STCs; more specifically, timevarying spaceonly codes. This new class is referred to as EMI codes. Full diversity is proven in terms of outage probability, for the case where the number of receive antennas is larger than or equal to the number of transmit antennas, and is numerically verified in terms of outage and word error probability using LDPC codes.  [Show abstract] [Hide abstract]
ABSTRACT: Multiple antenna (MIMO) devices are widely used to increase reliability and information bit rate. Optimal error rate performance (full diversity and large coding gain), for unknown channel state information at the transmitter and for maximal rate, can be achieved by approximately universal spacetime codes, but comes at a price of large detection complexity, infeasible for most practical systems. We propose a new coded modulation paradigm: errorcorrection outer code with spaceonly but timevarying precoder (as inner code). We refer to the latter as Ergodic Mutual Information (EMI) code. The EMI code achieves the maximal multiplexing gain and full diversity is proved in terms of the outage probability. Contrary to most of the literature, our work is not based on the elegant but difficult classical algebraic MIMO theory. Instead, the relation between MIMO and parallel channels is exploited. The theoretical proof of full diversity is corroborated by means of numerical simulations for many MIMO scenarios, in terms of outage probability and word error rate of LDPC coded systems. The fulldiversity and fullrate at low detection complexity comes at a price of a small coding gain loss for outer coding rates close to one, but this loss vanishes with decreasing coding rate.  [Show abstract] [Hide abstract]
ABSTRACT: Multiple antennas are used to increase reliability and bit rate for a given bandwidth. For a fixed transmission rate, discrete input alphabets and without channel state information at the transmitter, optimal spacetime codes (STCs) achieving both gains (full rate and full diversity) are well known. However, the complexity of maximum likelihood decoding increases exponentially with the number of space and time dimensions of the STC. Previous work reducing the complexity of decoding STCs has focused on the decoding algorithm, because the dimensions of the STC cannot be reduced without losing rate or diversity for uncoded communication. However, for coded communication (assuming the presence of an outer code), the dimensions of the STC may be reduced. We propose a new fullrate and fulldiversity suboptimal timevarying spaceonly code, adding a new dimension to the work on complexity reduction. Full diversity is proved in terms of the outage probability. 
Conference Paper: On the ergodic rate for computeandforward
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ABSTRACT: A key issue in computeandforward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z[i]n to a line in the ndimensional complex Euclidean space, within a bounded region around the origin. We then use the complex version of the LLL lattice basis reduction (CLLL) algorithm to provide a reduced complexity suboptimal solution as well as an upper bound to the minimum distance of the lattice point from the line. Using this bound we are able to find a lower bound to the ergodic rate and a union bound estimate on the error performance of a lattice constellation used for lattice network coding. We compare performance of the CLLL with a more complex iterative optimization method as well as with a simple quantized search. Simulations show how CLLL can trade some performance for a lower complexity.  [Show abstract] [Hide abstract]
ABSTRACT: For a given channel instance and a fixed LDPC ensemble, a stability outage event is defined by the density evolution being unstable at the origin. The probability of such an event, referred to as Stability Outage Probability, is a useful lower bound for the word error rate. We formulate the stability outage probability for block fading channels and we introduce the stability diversity order. As a direct application, we show how the class of capacityachieving ensembles on the erasure channel is bounded away from the outage limit on a block fading channel. 
Article: Full diversity random LDPC codes
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ABSTRACT: The block fading (BF) channel is a useful model for various communication systems in urban environments. Fulldiversity errorcorrecting codes are required to approach the physical limits of the performance on BF channels. Lowdensity paritycheck (LDPC) codes are good errorcorrecting codes, but fulldiversity standard random LDPC codes for the BF channel are not known yet. We design fulldiversity random LDPC ensembles at infinite block length by optimizing the threshold in multiple points in the fading space, which takes into account the randomness of the fading. However, this is not sufficient to achieve fulldiversity at finite block length, because of stopping sets. We therefore propose a method to generate fulldiversity code instances at finite length so that stopping sets over information bits are avoided. The asymptotic and finite length word error rate performance is verified by means of density evolution and Monte Carlo simulations, respectively, confirming that fulldiversity standard random LDPC codes exist and perform well.  [Show abstract] [Hide abstract]
ABSTRACT: We study precoding for the outage probability minimization of block fading (BF) channels and BF relay channels. Recently, an upper bound on the outage probability with precoding was established for BF channels, but only for high instantaneous SNR. This upper bound is much easier to minimize than the actual outage probability, so that optimal precoding matrices can be determined without much computational effort. Here, we provide a proof for the upper bound on the outage probability at low instantaneous SNR. Next, the structure of the precoding matrix is simplified so that it can be easily constructed for an arbitrary number of blocks in the BF channel. Finally, we apply this technique to cooperative communications.  [Show abstract] [Hide abstract]
ABSTRACT: Expectationmaximization (EM) based iterative algorithms are investigated in order to estimate the impulse response of a frequencyselective multipath channel in a coded OFDM system. Two ways of choosing the EM complete data are compared: a complete data built from observations and transmitted symbols (CLEM) and a complete data chosen by decomposing noise and observation components (NCDEM). Both CLEM and NCDEM algorithms are derived for a coded OFDM system. The rate of convergence of both EM algorithms is theoretically determined. It is found that the rate of convergence of CLEM is independent from the number of channel taps at high signaltonoise ratio (SNR), while that of NCDEM varies with the number of taps. It is shown that CLEM converges in a few iterations. Furthermore, considering the complexity per iteration, CLEM has a lower complexity than its counterpart. We also establish a CramerRao bound (CRB) for coded OFDM transmission. Simulation results show that CLEM has a good performancecomplexity tradeoff and it achieves the CRB.
Publication Stats
4k  Citations  
71.88  Total Impact Points  
Top Journals
Institutions

20072014

Texas A&M University at Qatar
Ad Dawḩah, Baladīyat ad Dawḩah, Qatar


2013

Pakistan Education Centre Doha Qatar
Ad Dawḩah, Baladīyat ad Dawḩah, Qatar


2010

Central University of Punjab
BUP, Punjab, India


20092010

Texas A&M University
College Station, Texas, United States 
Ghent University
 Department of Telecommunications and Information
Gent, VLG, Belgium


2006

Ecole Normale Supérieure de Paris
Lutetia Parisorum, ÎledeFrance, France


20052006

University of Utah
 Department of Electrical and Computer Engineering
Salt Lake City, Utah, United States 
École nationale supérieure de chimie de Paris
Lutetia Parisorum, ÎledeFrance, France 
Institut d'Electronique et des Télécommunications de Rennes
Roazhon, Brittany, France


19962006

École des Neurosciences de Paris ÎledeFrance
Lutetia Parisorum, ÎledeFrance, France


20022005

France Télécom
Lutetia Parisorum, ÎledeFrance, France


2001

Alcatel Lucent
Lutetia Parisorum, ÎledeFrance, France
