J.J. Boutros

Université de Cergy-Pontoise, 95001 CEDEX, Ile-de-France, France

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Publications (136)71.91 Total impact

  • Source
    Amin Sakzad, Emanuele Viterbo, Joseph Jean Boutros, Yi Hong
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    ABSTRACT: The compute-and-forward (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 quasi-optimal 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 degrees-of-freedom (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 low-complexity 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.
    04/2014;
  • Source
    Yang Liu, L. Brunel, J.J. Boutros
  • Amin Sakzad, Emanuele Viterbo, Joseph Jean Boutros, Yi Hong
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    ABSTRACT: In this work, we propose phase precoding for the compute-and-forward (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 quasi-optimal 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.
    01/2014;
  • N. di Pietro, G. Zemor, J.J. Boutros
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    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.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013
  • J.J. Boutros, E. Biglieri
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    ABSTRACT: This work investigates polar coding for block-fading 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 fading-plane 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.
    Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on; 01/2013
  • N. di Pietro, J.J. Boutros, G. Zemor, L. Brunei
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    ABSTRACT: A new family of integer lattices built from Construction A and non-binary low-density parity-check (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.
    Information Theory and Applications Workshop (ITA), 2013; 01/2013
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    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 space-time codes, but comes at a price of large detection complexity, infeasible for most practical systems. We propose a new coded modulation paradigm: error-correction outer code with space-only but time-varying 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 full-diversity and full-rate 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.
    05/2012;
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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 without channel state information at the transmitter, optimal space-time 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 full-rate and full-diversity suboptimal time-varying space-only code, adding a new dimension to the work on complexity reduction. Full diversity is proved in terms of the outage probability.
    01/2012;
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    ABSTRACT: We consider the use of lattice codes over Eisenstein integers for implementing a compute-and-forward protocol in wireless networks when channel state information is not available at the transmitter. We prove the existence of a sequence of infinite-dimensional 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 non-binary low density parity check code with a modulation scheme derived from the ring of Eisenstein integers.
    Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on; 01/2012
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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 space-time 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 error-correcting code with any coding rate. We propose a new class of full-rate full-diversity STCs; more specifically, time-varying space-only 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.
    Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on; 01/2012
  • D. Duyck, J.J. Boutros, M. Moeneclaey
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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 Low-Density Parity-Check (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 bit-interleaved coded modulation with iterative decoding (BICM-ID). This work uses precoding to optimize BICM-ID 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 error-correcting code yielding a WER that closely approaches this minimum outage probability. Using a geometric approach, the off-line 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.
    IEEE Transactions on Wireless Communications 01/2012; 11(7):2457-2467. · 2.42 Impact Factor
  • N. di Pietro, J.J. Boutros, G. Zemor, L. Brunel
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    ABSTRACT: We describe a new family of integer lattices built from construction A and non-binary LDPC codes. An iterative message-passing 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 (2004-2005). 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 real-valued message passing.
    Information Theory Workshop (ITW), 2012 IEEE; 01/2012
  • A. Sakzad, E. Viterbo, Yi Hong, J. Boutros
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    ABSTRACT: A key issue in compute-and-forward 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 n-dimensional 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.
    Network Coding (NetCod), 2012 International Symposium on; 01/2012
  • Source
    Dieter Duyck, Joseph Jean Boutros, Marc Moeneclaey
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    ABSTRACT: The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, full diversity on a block fading channel can be achieved without error-correcting code. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. Using a geometric approach, this paper establishes simple upper bounds on the outage probability, the minimization of which yields to precoding matrices that achieve very good performance. For discrete alphabets, it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing the coding gain.
    IEEE Transactions on Information Theory 03/2011; · 2.62 Impact Factor
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    Yang Liu, Loïc Brunel, Joseph Jean Boutros
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    ABSTRACT: Expectation-maximization (EM) based iterative algorithms are investigated in order to estimate the impulse response of a frequency-selective 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 (CL-EM) and a complete data chosen by decomposing noise and observation components (NCD-EM). Both CL-EM and NCD-EM 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 CL-EM is independent from the number of channel taps at high signal-to-noise ratio (SNR), while that of NCD-EM varies with the number of taps. It is shown that CL-EM converges in a few iterations. Furthermore, considering the complexity per iteration, CL-EM has a lower complexity than its counterpart. We also establish a Cramer-Rao bound (CRB) for coded OFDM transmission. Simulation results show that CL-EM has a good performance-complexity trade-off and it achieves the CRB.
    IEEE Transactions on Wireless Communications 01/2011; 10:3185-3195. · 2.42 Impact Factor
  • Source
    Dieter Duyck, Joseph J. Boutros, Marc Moeneclaey
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    ABSTRACT: The block fading (BF) channel is a useful model for various communication systems in urban environments. Full-diversity error-correcting codes are required to approach the physical limits of the performance on BF channels. Low-density parity-check (LDPC) codes are good error-correcting codes, but full-diversity standard random LDPC codes for the BF channel are not known yet. We design full-diversity 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 full-diversity at finite block length, because of stopping sets. We therefore propose a method to generate full-diversity 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 full-diversity standard random LDPC codes exist and perform well.
    01/2011;
  • Dieter Duyck, Joseph Jean Boutros, Marc Moeneclaey
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    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 capacity-achieving ensembles on the erasure channel is bounded away from the outage limit on a block fading channel.
    IEEE Communications Letters 01/2011; 15:1231-1233. · 1.16 Impact Factor
  • Source
    Dieter Duyck, Joseph J. Boutros, Marc Moeneclaey
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    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.
    01/2011;
  • D. Duyck, J.J. Boutros, M. Moeneclaey
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    ABSTRACT: The block fading channel model is very useful for many systems in urban environments. When striving for high performance implying high rate, full-diversity and excellent coding gain, coded modulations have to be used. When linear precoding is used, error-correcting codes can focus on achieving a high coding gain and are not constrained in coding rate so that no bandwidth is sacrificed. However, optimal precoding schemes for coded modulations on block fading channels are not known because of the inability to deal with the randomness of the fading gains. We study coded modulations for block fading channels in the fading space. This geometric approach yields more insight and allows to take into account the randomness of the fading. It can be used to generate the system parameters so that the word error rate performance approaches the outage probability closely.
    Communications and Vehicular Technology in the Benelux (SCVT), 2010 17th IEEE Symposium on; 12/2010
  • I. Andriyanova, E. Biglieri, J.J. Boutros
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    ABSTRACT: This paper<sup>1</sup> presents our investigation on iterative decoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in [1] and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes. Also, we show analytically that, in the case of 2 fading blocks, the iterative threshold γ<sup>*</sup><sub>root</sub> of Root-LDPC codes is proportional to (α<sub>1</sub>α<sub>2</sub>)<sup>-1</sup>, where α<sub>1</sub> and α<sub>2</sub> are corresponding fading gains. From this result, the full diversity property of Root-LDPC codes immediately follows.
    Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on; 11/2010

Publication Stats

3k Citations
71.91 Total Impact Points

Institutions

  • 2010
    • Université de Cergy-Pontoise
      95001 CEDEX, Ile-de-France, France
  • 2009–2010
    • Ghent University
      • Department of Telecommunications and Information
      Gent, VLG, Belgium
  • 2008–2010
    • Cea Leti
      Grenoble, Rhône-Alpes, France
  • 2007–2010
    • Texas A&M University at Qatar
      Ad Dawḩah, Ad Dawḩah, Qatar
  • 2008–2009
    • Texas A&M University
      • Department of Electrical and Computer Engineering
      College Station, Texas, United States
  • 2002–2009
    • France Télécom
      Lutetia Parisorum, Île-de-France, France
  • 2005–2007
    • University of Utah
      • Department of Electrical and Computer Engineering
      Salt Lake City, UT, United States
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
    • Institut d'Electronique et des Télécommunications de Rennes
      Roazhon, Brittany, France
  • 2006
    • École nationale supérieure de chimie de Paris
      Lutetia Parisorum, Île-de-France, France
    • Institut Fresnel
      Marsiglia, Provence-Alpes-Côte d'Azur, France
  • 1996–2006
    • École des Neurosciences de Paris Île-de-France
      Lutetia Parisorum, Île-de-France, France
    • Ecole Normale Supérieure de Paris
      Lutetia Parisorum, Île-de-France, France
  • 2003
    • École Supérieure d'Electricité
      Gif, Île-de-France, France
  • 2001
    • Alcatel Lucent
      Lutetia Parisorum, Île-de-France, France