In this paper, we propose a new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan. These multi-kernel polar codes allow for more flexibility in terms of the code length and for various new design principles. Next to the common reliability design, we provide a design to maximize the minimal distance and a hybrid design combining reliability and distance properties. Numerical results demonstrate the advantage of multi-kernel polar codes under the new design principles compared to punctured and shortened Arikan polar codes.

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.

Lemma 1in the above-titled paper[1]only holds for a center$\mathbf {c}=\mathbf {0}$. Therefore,Lemma 1and its preceding paragraph should be replaced by:

We propose a coding scheme that achieves the capacity of the compound MIMO channel with algebraic lattices. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. These techniques, along with algebraic properties of the proposed lattices, are then used to construct a sub-optimal de-coupled coding scheme that achieves a constant gap to compound capacity by decoding in a lattice that does not dependent on the channel realization. The gap is characterized in terms of algebraic invariants of the code and is shown to be significantly smaller than previous schemes in the literature. We also exhibit alternative algebraic constructions that achieve the capacity of ergodic (SISO) fading channels.

The construction of deletion codes for the editing metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of lattices' translates. These lattices, in turn, are obtained from Construction A applied to binary codes and Z4-codes. A lower bound on the size of our codes for the Manhattan distance are obtained through generalized theta series of the corresponding lattices. For any fixed number of deletions, provided the number of runs is large enough our method supplies a correction technique. For fixed number of runs and binary sequence length large our lattice construction is shown to be tight up to constants.

In this paper, we propose a construction for multi-kernel polar codes based on the maximization of the minimum distance. Compared to the original construction based on density evolution, our new design shows particular advantages for short code lengths, where the polarization effect has less impact on the performance than the distances of the code. We introduce and compute the minimum-distance profile and provide a simple greedy algorithm for the code design. Compared to state-of-the-art punctured or shortened Arikan polar codes, multi-kernel polar codes with our new design show significantly improved error-rate performance.

In this work, we introduce β-expansion, a notion borrowed from number theory, as a theoretical framework to study fast construction of polar codes based on a recursive structure of universal partial order (UPO) and polarization weight (PW) algorithm. We show that polar codes can be recursively constructed from UPO by continuously solving several polynomial equations at each recursive step. From these polynomial equations, we can extract an interval for β, such that ranking the synthetic channels through a closed- form β-expansion preserves the property of nested frozen sets, which is a desired feature for low- complex construction. In an example of AWGN channels, we show that this interval for β converges to a constant close to 1.1892 when the code block-length trends to infinity. Both asymptotic analysis and simulation results validate our theoretical claims.

Previous approaches to compute-and-forward (C&F) are mostly based on quantizing channel coefficients to integers. In this work, we investigate the C&F strategy over block fading channels using Construction A over rings, so as to allow better quantization for the channels. Advantages in decoding error probabilities and computation rates are demonstrated, and the construction is shown to outperform the C&F strategy over the integers Z.

Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC). It has been proven that decoding an integer linear combination of the transmitted codewords enables higher data rates compared to decoding the messages individually. Recent work of Gasptar et al. proposed a new multiple access channel technique that they called Compute- and-Forward Multiple Access Channel (CFMA). The authors proved that, in the case of a two-user MAC and without time sharing, the entire capacity region is achieved using CFMA and a single-user decoder for signal to noise ratios above 1 + √2. Throughout this paper, we will work within the Compute- and-Forward framework. The strategy relies on lattice codes, here we will construct lattices using a multi-level coding based construction called construction D. To decode the lattice points, a multi-stage decoder (MSD) should be implemented at the receiver part. In this paper, we propose a new decoding strategy that helps to perform the standard MSD algorithm in a less complex way. The new technique is called Binary Subchannel Decomposition (BSCD). Since, we make use of MSD, we need at each level of the decoder to compute soft-inputs: Log-Likelihood ratios. However the calculations are very complex since we must compute infinite sums of exponentials at each stage. Hereinafter we give efficient LLR approximation for multi-stage decoders. Simulation results about the performance of BSCD are included and compared to the performance of the standard multi-stage decoder.

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the simplex code and duals of certain Bose--Chaudhuri--Hocquenqhem codes. Our results are based on the trace representation of cyclic codes.

In this paper, we propose a space time code construction with a symbol rate of two for free space optical multiple input multiple output (FSO-MIMO) communication systems. Unlike the radio-frequency space time coding design that deals with complex symbols holding phase and magnitude information, the phase detection in wireless optical communications remains very challenging. This restricts optical MIMO codes to carry positive magnitude information belonging to a finite range. To meet these requirements, we propose to design the FSO-MIMO codes considering first the whole real space R, followed by a bipolar to unipolar conversion to fit in the intensity margin. We consider the MIMO configurations with two or four transmitters (lasers). We base our shape-preserving construction on quadratic extension fields that linearly combine the real symbols to form a full diversity space time code with a symbol rate equal to two. For each configuration, we show how to optimize the choice of the algebraic field numbers to jointly optimize the non-vanishing code determinant and the bipolar to unipolar attenuation factor.

We propose a lattice coding scheme that achieves the capacity of the compound block-fading channel. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. A by-product of our results is a refined analysis of the probability of error of the lattice Gaussian distribution in the AWGN channel.

In this work we show that algebraic lattices constructed from error-correcting codes achieve the ergodic capacity of the fading channel. The main ingredients for our construction are a generalized version of the Minkowski-Hlawka theorem and shaping techniques based on the lattice Gaussian distribution. The structure of the ring of integers in a number field plays an important role in the proposed construction. In the case of independent and identically distributed fadings, the lattices considered exhibit full diversity and an exponential decay of the probability of error with respect to the blocklength.

In this paper, we propose a multilevel lattice construction, employing binary Reed-Muller codes, for the Rayleigh block fading channel. The construction is performed on a binary two-dimensional lattice partition chain, and Reed-Muller codes are chosen according to capacity rule. The lattice construction based on number-theoretical concepts is explained, and the system's performance is shown for various codeword lengths.

In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over n-bit vectors taking m-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT) of a binary function f : G → ℜ, where G = (F2n, +) is the group of n bit vectors with bitwise modulo two addition +, and ℜ is a finite commutative ring of characteristic 2. Using the specific group structure of G and a sequence of nested subgroups of G, we define the fast TMFT and its inverse. Since the image ℜ of the binary functions is a ring, we can define the convolution between two functions f : G → ℜ. We then provide the TMFT properties, including the convolution theorem, which can be used to efficiently compute convolutions. Finally, we derive the complexity of the fast TMFT and the inverse fast TMFT.

We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN channel. We propose a coding strategy based on lattice coset encoding. We define the secrecy gain as a design criterion for wiretap lattice codes, expressed in terms of the lattice theta series, which characterizes Eve's confusion as a function of the channel parameters. The secrecy gain is studied for even unimodular lattices, and an asymptotic analysis shows that it grows exponentially in the dimension of the lattice. Examples of wiretap lattice codes are given.

In this paper we introduce the two-modular Fourier transform of a binary function f : R → R defined over a finite commutative ring R = F2[X]/ϕ(X), where F2[X] is the ring of polynomials with binary coefficients and ϕ(X) is a polynomial of degree n, which is not a multiple of X. We also introduce the corresponding inverse Fourier transform. We then prove the corresponding convolution theorem.

Nested lattices Ae⊂ Abhave previously been studied for coding in the Gaussian wiretap channel and two design criteria, namely, the secrecy gain and flatness factor, have been proposed to study how the coarse lattice Aeshould be chosen so as to maximally conceal the message against the eavesdropper. In this paper, we study the connection between these two criteria and show the secrecy-goodness of even unimodular lattices, which means exponentially vanishing flatness factor as the dimension grows.

This paper considers shifted inverse determinant sums arising from the union bound of the pairwise error probability for space-time codes in multiple-antenna fading channels. Previous work by Vehkalahti et al. focused on the approximation of these sums for low multiplexing gains, providing a complete classification of the inverse determinant sums as a function of constellation size for the most well-known algebraic space-time codes. This work aims at building a general framework for the study of the shifted sums for all multiplexing gains. New bounds obtained using dyadic summing techniques suggest that the behavior of the shifted sums does characterize many properties of a lattice code such as the diversity-multiplexing gain trade-off, both under maximum-likelihood decoding and infinite lattice naive decoding. Moreover, these bounds allow to characterize the signal-to-noise ratio thresholds corresponding to different diversity gains.

In this presentation we are interested in coding for wiretap wireless channels. First part is devoted to design criteria, second part will deal with the codes themselves. Nested lattices are the main ingredients to be used. We start with the Gaussian wiretap channel where it is shown that theta series have to be minimized. Then we give some ideas in the case of fading wiretap channels. In part two, we give some results that help finding good lattice codes of moderate and high length. Part of this work was supported by FP7 project PHYLAWS (EU FP7-ICT 317562).

In this paper, we investigate the achievable semantic secrecy rate of existing lattice coding schemes, proposed in [6], for both the mod-Λ Gaussian wiretap and the Gaussian wiretap channels. For both channels, we propose new upper bounds on the amount of leaked information which provide milder sufficient conditions to achieve semantic secrecy. These upper bounds show that the lattice coding schemes in [6] can achieve the secrecy capacity to within ½ln e/2 nat for the mod-Λ Gaussian and to within ½(1 - ln (1 + SNRe/ SNRe+1)) nat for the Gaussian wiretap channels where SNReis the signal-to-noise ratio of Eve.

We propose a new coding scheme using only one lattice that achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, which is provable for signal-to-noise ratio SNR > e at present. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but otherwise does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which involves a quantization good lattice as well as an AWGN-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error lattice decoding is almost the same as that of Erez and Zamir, for any rate up to the AWGN channel capacity. We introduce the notion of good constellations, which carry almost the same mutual information as that of continuous Gaussian inputs. We also address the implementation of Gaussian shaping for the proposed lattice Gaussian coding scheme.

We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor, which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No a priori distribution of the message is assumed, and no dither is used in our proposed schemes.

In this paper we study the performance of Barnes-Wall lattices in a symmetric interference channel, under different types of interference. We are inspired by the work of Jafar [1], in which a scheme is proposed for each type of interference, using a base Q expression for the transmitted signals. This is similar to the multilevel structure of Barnes-Wall lattices. With the advantage of their good performance and the extension in bigger dimensions that using lattices implies, we propose to use Barnes-Wall lattices to improve the performance of each user, under lattice alignment in a symmetric interference channel.

We propose a new coding scheme using only one lattice that, under lattice decoding, achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel, when the signal-to-noise ratio SNR > 3. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which additionally involves a quantization-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error (MMSE) lattice decoding is almost the same as that of Poltyrev's coding over an infinite lattice, for any rate up to the AWGN channel capacity.

As a first step towards distributed computations in a wireless network, we introduce ideal lattices, that is lattices built over an ideal of a ring of integers in a number field, as a tool for constructing lattice codes at the physical layer. These lattices are not only additive groups as all lattices, but they are also equipped with a multiplication, which enables polynomial operations at each node of the wireless network. In this paper, we show how some of these ideal lattices can be constructed from polynomial codes (generalization of cyclic codes) via Construction A, and illustrate how these lattices enable multiplication.

We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use an infinite lattice codebook, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is treated similarly, and fast fading channels are derived as a particular case. The Alamouti code is carefully studied as an illustration of the analysis provided.

We address the application of Barnes-Wall (BW) lattice codes for communication over additive white Gaussian noise (AWGN) channels. We introduce Construction A^prime of complex BW lattices that makes new connection between linear codes over polynomial rings and lattices. We show that Construction A^prime of BW lattices is equivalent to the multilevel construction from Reed-Muller codes proposed by Forney. To decode the BW lattice code, we adapt the low-complexity sequential BW lattice decoder (SBWD) proposed by Micciancio and Nicolosi. First we study the error performance of SBWD for decoding the infinite lattice, and demonstrate that it is powerful in making correct decisions well beyond the packing radius. Subsequently, we use the SBWD to decode lattice codes through a novel noise trimming technique, where the received vector is appropriately scaled before applying the SBWD. We show that the noise trimming technique is most effective for decoding BW lattice codes in smaller dimensions, while the gain diminishes for decoding codes in larger dimensions.

Dense lattice packings can be obtained via the well-known Construction A from binary linear codes. In this paper, we use an extension of Construction A called Construction A' to obtain Barnes-Wall lattices from linear codes over polynomials rings. To obtain the Barnes-Wall lattice BW2min C2mfor any m ≥ 1, we first identify a linear code C2mover the quotient ring Um= F2[u]/umand then propose a mapping ψ : Um→ Z[i] such that the code L2m= ψ (C2m) is a lattice constellation. Further, we show that L2mhas the cubic shaping property when m is even. Finally, we show that BW2mcan be obtained through Construction A' as BW2m= (1 + i)mZ[i]2m⊕ L2m.

We consider a wiretap scenario where the main channel and eavesdropper's channel are modulo lattice Gaussian channels. We prove that nested lattice codes can achieve strong secrecy for this model, which gives considerable insights to tackle the genuine Gaussian wiretap channel. The key tool in our proof is an L1convergence result for the conditional output distributions corresponding to different messages, which follows from the properties of the lattice Gaussian measure. No constraint on the a priori distribution of the message is imposed, which means that the proposed scheme is actually semantically secure. We not only show the existence of lattice codes that are good for secrecy, but also propose the flatness factor as a design criterion.

In this paper we consider the error performance analysis of lattice alignment for the many-to-one interference channel. An upper bound on the error probability for the first receiver when lattice codes are used is derived. More precisely, we consider the case of joint maximum-likelihood (ML) decoding of the desired signal and the sum of interfering signals, derive the union bound for the error probability in terms of the theta series of these lattices, and show that it is related to the flatness factor.

Distributed source coding addresses the compression of correlated sources without communication links among them. This paper is concerned with the Wyner-Ziv problem: coding of an information source with side information available only at the decoder in the form of a noisy version of the source. Both the problems of theoretical analysis and code design are addressed in the framework of multi-dimensional nested lattice coding. For theoretical analysis, accurate computation of the rate-distortion function is given under the high-resolution assumption, and a new upper bound using the derivative of the theta series is derived. For practical code design, several low-complexity techniques are proposed. Compared to the existing Slepian-Wolf coded nested quantization for Wyner-Ziv coding based on one or two-dimensional lattices, our proposed multi-dimensional lattice coding can offer better performance at arguably lower complexity, since it does not require the second stage of Slepian-Wolf coding.

The design of perfect space time codes constructed from cyclic division algebra (CDA) on the quasi-static MIMO channel has received lots of attention in industry over the last few years. However, the recent standards that use multiple antennas terminals such as IEEE 802.11n, IEEE 802.16e or LTE are based on more realistic assumptions involving the use of outer codes and multi-taps channels. In this paper, the question regarding the utility of using a high dimensional modulation schemes such as space time codes in a standard context is addressed. For this, we evaluate the performance of the perfect space time codes in term of an upper-bound on the pairwise error probability, and we compare it to the one of simple spatial division multiplexing (SDM) schemes. Finally, simulation results considered in the context of IEEE 802.11n show that the 2 × 2 MIMO perfect code, i.e. the golden code performs relatively similarly as the SDM scheme in the presence of a good outer code.

It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an appropriate outer code. When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding, more precisely, by taking the quotient of the algebra by a two-sided ideal which leads to matrices over finite alphabets for the outer code. In this paper, we show that the determinant criterion induces various metrics on the outer code, such as the Hamming and Bachoc distances. When n = 2, partitioning the 2×2 Golden code by using an ideal above the prime 2 leads to consider codes over either M2(F2) or M2(F2[i]), both being noncommutative alphabets. By identifying them as algebras over a finite field or a finite ring respectively, we establish an unexpected connection with classical error-correcting codes over F4and F4[i]. Matrix rings of higher dimension, suitable for 3×3 and 4×4 perfect codes, give rise to more complex examples.

In this paper, we study the feasibility of the interference alignment (IA) scheme for the selective fading interference channel with time-frequency selective links. Unlike the frequency selective channel case, we show here that, for the scalar time-frequency (TF) selective underspread channels, there is no need to scale the bandwidth as the number of users. However, a constraint on the delay-Doppler spread of the channel itself is required. A physical interpretation of this condition in the time-frequency domain is provided and is shown to be easily satisfied in practical system. Our results are based on the polynomial channel decomposition that we derive for the TF channel with large signal duration and bandwidth.

In a recent work, Nazer and Gastpar proposed the compute-and-forward strategy as a physical-layer network coding scheme. They described a code structure based on nested lattices whose algebraic structure makes the scheme reliable and efficient. In a more recent paper, Feng et al. introduced an algebraic approach to the lattice implementation. In this work, we consider some problems not addressed in already published works, mainly the ML decoding.

Secrecy gain has been proposed as a criterion to design wiretap lattice codes. Its analysis relies on the theta series of a lattice, which is closely related to the union bound on the decoding error probability. In this paper, theta series of trellis codes are computed by using a modified transfer function originally for the union bound. We find that the low SNR region of the union bound dominates the secrecy gain. Numerical results show that trellis codes can achieve a similar or higher secrecy gain with less complexity compared to unimodular lattice codes.

Perfect space-time codes (STC) are optimal codes in their original construction for multiple-input multiple-output (MIMO) systems. Based on cyclic division algebras (CDA), they are full-rate, full-diversity codes, have non-vanishing determinants (NVD) and hence achieve diversity-multiplexing tradeoff (DMT). In addition, these codes have led to optimal distributed space-time codes when applied in cooperative networks under the assumption of perfect synchronization between relays. However, they lose their diversity when delays are introduced and thus are not delay-tolerant. In this paper, using the cyclic division algebras of perfect codes, we construct new codes that maintain the same properties as perfect codes in the synchronous case. Moreover, these codes preserve their full-diversity in asynchronous transmission.

It is well known that the presence of double scattering degrades the performance of a MIMO channel, in terms of both the multiplexing gain and the diversity gain. In this paper, a closed-form expression of the diversity-multiplexing tradeoff (DMT) of double scattering MIMO channels is obtained. It is shown that, for a channel withnTtransmit antennas,nRreceive antennas. andnSscatterers, the DMT only depends on the ordered version of the triple (nT,nS,nR) , for arbitrarynT,nSandnR. The condition under which the double scattering channel has the same DMT as the single scattering channel is also established.

In relay networks, a conventional way to exploit spatial diversity is to introduce distributed space-time processing at the relays. In our work, we show that even simple time-varying distributed rotation can recover spatial diversity. The main idea is to convert the inherent spatial diversity to time diversity by creating an artificial fast fading channel. It turns out that the proposed framework is both tractable from the theoretical point of view and simple from the practical point of view. Furthermore, the framework is quite general and can be applied to a wide range of linear/nonlinear relaying strategies. As applications, we first propose a linear relaying scheme called rotate-and-forward for multiple-antenna two-hop layered networks. It is shown that, in some non-trivial setting, this scheme outperforms existing schemes and achieves the optimal diversity-multiplexing tradeoff. The second application is a decode-and-forward scheme based on the same idea in the single-antenna multiple-relay channel. It is shown to achieve the maximum diversity with low signaling complexity.

We propose the notion of secrecy gain as a code design criterion for wiretap lattice codes to be used over an additive white Gaussian noise channel. Our analysis relies on the error probabilites of both the legitimate user and the eavesdropper. We focus on geometrical properties of lattices, described by their theta series, to characterize good wiretap codes.

In the authors introduced a lattice invariant called “Secrecy Gain” which measures the confusion experienced by a passive eavesdropper on the Gaussian Wiretap Channel. We study, here, the behavior of this invariant for unimodular lattices by using tools from Modular Forms and show that, for some families of unimodular lattices, indexed by the dimension, the secrecy gain exponentially goes to infinity with the dimension.

In this paper, we extend the non-vanishing determinant (NVD) criterion to the selective fading channel case. A new family of split NVD parallel codes, that satisfies this design criterion, is proposed to achieve the optimal diversity multiplexing tradeoff (DMT) derived by Coronel and Bölcskei, IEEE ISIT, 2007. This result is of significant interest not only in its own right, but also because it settles a long-standing debate in the literature related to the optimal DMT of selective fading channels.

The goal of our work is to limit in-band interference in wireless communication systems. Based on a three-regime interference classifier, we propose a novel distributed inter-cell power allocation algorithm where each cell computes by an iterative process its minimum power budget to meet its local quality of service (QoS) constraints. Analytical results show how our proposal permits to notably reduce both transmission power and harmful effects of in-band interference, while meeting QoS constraints of users in each cell.

Lattice reduction algorithms, such as the LLL algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in MIMO communications. In this paper we introduce a new kind of lattice reduction-aided decoding technique, called augmented lattice reduction, which recovers the transmitted vector directly from the change of basis matrix, and therefore doesn't entail the computation of the pseudo-inverse of the channel matrix or its QR decomposition. We prove that augmented lattice reduction attains the maximum receive diversity order of the channel; simulation results evidence that it significantly outperforms LLL-SIC detection without entailing any additional complexity.

In this paper, we consider the layered two-hop relay channel, operating under the linear rotate-and-forward (RF) scheme, where the relays rotate the received signal before its retransmission. In this work, a limited feedback channel is considered between the relays and the destination. The destination finds the optimal rotation vector and feeds it back to the relays. We propose an iterative algorithm to find this optimal rotation vector. The proposed algorithm is shown to have optimal performance with low complexity.

Perfect Space-Time Codes (STC) are full-rate, full-diversity codes originally proposed for Multiple Input Multiple Output (MIMO) systems. Based on Cyclic Division Algebras (CDA), they have non-vanishing determinants and hence achieve the Diversity-Multiplexing Tradeoff (DMT). In addition, these codes have led to optimal distributed Space-Time Codes when applied in cooperative networks under the assumption of perfect synchronization between relays. However, they lose their diversity when delays are introduced and thus are not delay-tolerant. In this paper, using the cyclic division algebras of perfect codes, we construct new codes that maintain the same properties as perfect codes in the synchronous case. Moreover, these codes preserve their full-diversity in asynchronous transmission.

The goal of our work is to limit inter-cell interference in two hops cooperative communication systems.We propose to exploit the standard half-duplex limitation of relays so as to coordinate in time and frequency the resource allocation of a cluster of neighbor cells, and then to adapt resource allocation to changes in the communication context. Simulation results show how our proposed allocation modes permit to outperform classical modes in terms of cooperation effectiveness, power consumption and perceived Quality of Service (QoS).

The goal of our work is to limit in-band inter-cell interference in wireless communication cellular systems. Based on interference classification techniques, we propose a novel centralized inter-cell power allocation algorithm which computes the minimum power budget required in each cell to meet its local quality of service (QoS) constraints. Both analytical and numerical results applied to cellular networks show how our algorithm permits to notably reduce both power budget and harmful effects of in-band inter-cell interference, while meeting QoS constraints of users in each cell.

An efficient algorithm for bit-loading in multicarrier systems is proposed based upon an allocation rhythm/order underlying the classical optimal greedy bit-allocation procedure. An accurate complexity comparison in terms of the exact number of execution cycles over a processor is made with the classical Greedy solution along with another recently proposed optimal bit-loading algorithm. Simulation results verify the significant complexity advantage of our algorithm with no loss in performance.

This paper addresses the Margin Adaptive (MA) problem in MIMO OFDMA multi-cell networks. Resource allocation is distributed within each Base Station. Two cases are considered: full CSIT, and statistical CSIT. In both cases, a distributed convergence criterion for power control is determined and included within iterative power allocation. In the statistical CSIT case, an approximate analytical expression is obtained for the outage capacity, as a function of the SNR and the outage probability. It turns the MA problem into a convex optimization problem, and is valid at practical SNR and outage capacity values, for several antenna configurations. The proposed methods avoid power divergence situations at any load, and are consequently more efficient than iterative water-filling to solve the MA problem.

Lattice reduction algorithms, such as the Lenstra-Lenstra-Lovasz (LLL) algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in multiple-input multiple-output (MIMO) communications. A different approach, introduced by Kim and Park, allows to combine right preprocessing and detection in a single step by performing lattice reduction on an v{augmented channel matrix}. In this paper we propose an improvement of the augmented matrix approach which guarantees a better performance. We prove that our method attains the maximum receive diversity order of the channel. Simulation results evidence that it significantly outperforms LLL reduction followed by successive interference cancellation (SIC) while requiring a moderate increase in complexity. A theoretical bound on the complexity is also derived.

In this paper we introduce a new right preprocessing method for the decoding of 2 times 2 algebraic space-time codes, called algebraic reduction, which exploits the multiplicative structure of the code. The principle of the new reduction is to absorb part of the channel into the code, by approximating the channel matrix with an element of the maximal order of the code algebra. We prove that algebraic reduction attains the receive diversity when followed by a simple zero-forcing (ZF) detection. Simulation results for the golden code show that using minimum mean squared error generalized decision feedback equalization (MMSE-GDFE left preprocessing), algebraic reduction with simple ZF detection has a loss of only 3 dB with respect to optimal decoding.

We consider a multi-cell MIMO downlink (network MIMO) where B base-stations (BS) with M antennas, connected to a central station (CS), transmit K messages to K single-antenna user terminals (UT) simultaneously. Although many works have shown the potential benefits of network MIMO, the conclusion critically depends on the underlying assumption of perfect channel state information at transmitters (CSIT). In this paper, we propose an outage-efficient strategy that requires only partial CSIT. Namely, with side information of all UT's messages and local CSIT, each BS applies zero-forcing (ZF) beamforming in a distributed manner, which creates K parallel MISO channels. Based on the statistical knowledge of these parallel channels, the CS performs a robust power allocation that jointly minimizes the outage probability of K UTs and achieves a diversity gain of B(M - K + 1) per UT. Numerical results show that even with partial CSIT network MIMO can be beneficial by providing high data rates with a sufficient reliability to individual users.

In this paper, we study code constructions over the finite ring M2(F2), the ring of 2times2 matrices with coefficients in the finite field F2. We show how they can be related to classical codes over F4. We provide as application the design of outer codes for 2 times 2 space-time coded modulation, when the inner code is the so-called Golden code.

In this work, the multiple access channel (MAC) with asynchronous users is considered. Users are not allowed to cooperate together and do not have any channel side information. The code design criteria are first developed for this channel and a MAC coding scheme that verifies these criteria, i.e., delay tolerant code, is investigated. Simulation results confirms that the diversity of the proposed space-time codes is preserved in an asynchronous scenario.

In this paper, we consider the Multiple-Access channel with a non uniform energy distribution among users. We point out that, while a space-time code is optimal for the MAC in a balanced scenario, it could become suboptimal in an unbalanced scenario. No CSI is available at the transmitters that are initially assumed to have different energies. We investigate the use of an adapted coding scheme characterized by an unbalanced energy distribution among the symbols that helps compensating the system's unbalance. Numerical results illustrating the outage probability of the channel as well as the error probability of the proposed coding scheme for different power distributions are provided. We show that this unbalanced code is more appropriate in an unbalanced scenario and that it outperforms the best known coding scheme for the MAC.

In existing MIMO systems, either optimal or sub-optimal decoders can be used according to the required performance. However, the optimal decoders give ML performance but have very high complexity and the sub-optimal decoders give low complexity but poor performance. Moreover for ML decoding, the variable decoding time at a fixed SNR for the different channel realizations and also the big gap in the complexity between low and high SNRs represent a critical point for practical implementation. We propose here an adaptive decoder that allows to switch between optimal and sub-optimal decoders according to the channel realization and the system specifications. This decoder offers an almost constant complexity while keeping good performance.

In this paper, block-coded modulation is used to design a 2 times 2 multiple-input multiple-output (MIMO) space-time code for slow fading channels. The golden code is chosen as the inner code; the scheme is based on a set partitioning of the golden code using two-sided ideals whose norm is a power of two. In this case, a lower bound for the minimum determinant is given by the minimum Hamming distance. The description of the ring structure of the quotients suggests further optimization in order to improve the overall distribution of determinants. Simulation results show that the proposed schemes achieve a significant gain over the un-coded golden code.

In this work, we present a construction of a family of space-time block codes for a Multi-Access Amplify-and-Forward Relay channel with two users and a single half-duplex relay. It is assumed that there is no Channel Side Information at the transmitters and that they are not allowed to cooperate together. Using the Diversity Multiplexing Tradeoff as a tool to evaluate the performance, we prove that the proposed scheme is optimal in some sense. Moreover, we provide numerical results which show that the new scheme outperforms the orthogonal transmission scheme, e. g. time sharing and offers a significant gain.

In this work, the multiple transmit antennas multiple access channel is considered. A construction of a family of distributed space-time codes for this channel is proposed. No channel side information at the transmitters is assumed and users are not allowed to cooperate together. It is shown that the proposed code achieves the diversity multiplexing tradeoff of the channel. As an example, we consider the two-user MIMO-MAC channel. Simulation results show the significant gain offered by the new coding scheme compared to an orthogonal transmission scheme, e.g. time sharing.

In a broadcast channel with random packet arrival and transmission queues, the stability of the system is achieved by maximizing a weighted sum rate capacity with suitable weights that depend on the queue size. The weighted sum rate capacity using Dirty Paper Coding (DPC) and Zero Forcing (ZF) is asymptotically equivalent to the weighted sum capacity over parallel single-channels. In this paper, we study the Diversity Multiplexing Tradeoff (DMT) of the fading broadcast channel under a fixed weighted sum rate capacity constraint. The DMT of both identical and different parallel weighted MISO channels is first derived. Finally, we deduce the DMT of a broadcast channel using DPC and ZF precoders.

We consider a block coded modulation scheme for a 2 times 2 MIMO system over slow fading channels, where the inner code is the Golden Code. The scheme is based on a set partitioning of the Golden Code using two-sided ideals. A lower bound for the minimum determinant is given by the minimum Hamming distance. Performance simulations show that our GCRS schemes achieve a significant gain over the uncoded Golden Code.

In this paper, the selective time division multiple access (S-TDMA) strategy is studied in the downlink channel. This strategy consists in transmitting data to the user with the largest capacity. The diversity and multiplexing gains that can be achieved by this sub-optimal strategy are evaluated and then compared to the optimal gains over the broadcast channel. Codes construction is then proposed to achieve the diversity multiplexing tradeoff (DMT) of the S-TDMA. These codes are extended to the scenario of cooperating asynchronous broadcasting base stations where new codes that are suitable for this scenario are proposed and analyzed.

In this paper, we consider the isotropic fading broadcast channel. This channel refers to the case when no directional information is available at the transmitter side, and was studied by Jafar et al in. It was shown that the isotropic vector broadcast channel (BC-V) can be reduced to an equivalent scalar broadcast channel (BC-S). It is well known from [2]http://www.pimrc2008.org/ that BC-S is degraded in the same order as the channel magnitude. This implies that the optimal strategy that maximizes the sum capacity for BC-S and BCV consists on allocating the whole power to the strongest user. Based on these results, we derive in this paper the diversity multiplexing tradeoff (DMT) of the isotropic fading BC-S and BC-V, and we propose optimal schemes that achieve these DMT.

This paper addresses the weighted sum throughput maximization problem on the interference channel. It proposes a sub-optimal algorithm that enables to perform a distributed power allocation, which performs well at any SINR regime. The sub-optimal method consists of two phases: first, identify the links that should be set to zero, and then, operate in the high SINR regime for the remaining links. In the single channel case, this simple, fully distributed algorithm is shown to perform almost as well as the centralized optimal algorithm. In the multi-channel case, the algorithm is more efficient than iterative water-filling in order to decrease the buffer size.

Distributed space-time codes over two asynchronous relays are considered. First, we show that the space-time code proposed in [1] is suitable for asynchronous transmission over two relays. Using tools from division algebra, we study the quadratic form resulting from its determinant and we prove that this code has a non-vanishing determinant over all constellations carved from Zopf[i], and thus is optimal in the sense of diversity-multiplexing tradeoff [2]. Then, we propose a delay-tolerant code based on the Golden code [3] the full-rate full-diversity information lossless space-time code proposed for the MIMO channel, and we deduce the convenient unitary matrices to obtain the modified code. Applying these matrices to other MIMO codes, namely Tirkkonen-Hottinen [4] and Sezginer-Sari code [5], we infer new delay-tolerant codes. In addition of being suitable for asynchronous relay transmission, all the new codes have the same determinants as the old ones.

This paper deals with power allocation techniques for cooperative protocols where terminals are constrained by half-duplex assumption and average total network power. We propose a cooperation scheme based on the combination of hybrid cooperation strategies with an effective power allocation algorithm. Simulation results show that our proposal improves the outage performance while reducing the overall cooperation complexity.

This paper addresses inter-cell interference mitigation techniques in OFDMA cellular networks. It compares the performance results obtained with partial frequency reuse in the outer cell and with a proposed cooperative scheme based on relaying of the users in the outer cell. The proposed scheme uses cooperative diversity via a relaying protocol between the source base station and the closest base station, therefore reducing inter-cell interference. Subcarrier and power allocation can be implemented in a distributed way in each base station. Numerical results show that the same average inter-cell interference is achieved with cooperation as with a frequency reuse factor of 3, whereas cooperation leads to a lower rejection probability and higher sum throughput at medium to high load.

Cooperative diversity at a system level is a promising method to improve the performance of the users located at the border of cells in distributed cellular networks. In this paper, we propose a Quality-of-Service based resource allocation algorithm for downlink OFDMA, in which Base Stations trigger cooperative diversity for users requiring a minimum data rate. As Downlink cooperation increases the spectral efficiency for users at the border of the cells, it enables to decrease the power required for these users. The remaining Best Effort users can then be served with more power, therefore increasing their sum throughput. The proposed distributed method is compared with other resource allocation techniques, and proves to be very efficient for the users with both types of Quality of Service.

In this paper, we extend the Amplify-and-Forward cooperative diversity scheme to the context of impulse radio ultra wideband (IR-UWB). In particular, we present the construction of three families of minimal-delay and totally-real distributed algebraic space-time (ST) codes suitable for IR-UWB. The first family encodes adjacent symbols and is based on totally-real cyclic division algebras. The second family encodes the pulses used to transmit one information symbol and permits to achieve high performance levels with lower complexity. Both families of codes achieve full rate, full diversity with non-vanishing determinants for various number of relays. These schemes can be associated with pulse position modulation (PPM), pulse amplitude modulation (PAM) and hybrid pulse position and amplitude modulation (PPM-PAM). The third family of codes is information-lossless and does not require any pulse repetitions. It is specific to M-PPM-M'-PAM with M ges 3 and for all values of M'. Simulations performed over realistic indoor UWB channels are provided to verify the theoretical results.

This paper addresses downlink cooperation at a system level. Cooperation between base stations is an alternative to macrodiversity to provide QoS continuity in case of mobility. We propose a radio resource management strategy for the relay channel, made of relayed users identification, resource allocation and power control in an OFDMA-based system. Four scheduling methods are tested for power allocation in inter-cell interference environment: globally optimal, proportional fair, harmonic mean fair and max-min fair. Cooperation brings additional gain, both in terms of throughput and fairness, with all fair schedulers.

This paper deals with throughput oriented adaptive modulation and coding (AMC) techniques combined with cooperative protocols where terminals are constrained by half-duplex assumption and average total network power. We propose a novel hybrid cooperation protocol that switches from cooperative to non-cooperative transmission based on the momentary direct source-destination link quality. Then, we propose anhybridcooperativeAMCmechanism, which combines AMC with hybrid cooperation. Simulation results show that our proposal improves the average system performance and reduces the average cooperation signaling cost.

In this paper, we propose an application of cooperative system in the ad-hoc network. Based on 802.11a PHY, a compatible physical layer protocol Relay-SISO is introduced for the single-relay single-antenna system. Using Non-orthogonal Amplify-and-Forward scheme, the proposed protocol boosts quality of transmission while works at the same data rate as 802.11a with little additional preambles. Simulation results reveal the feasibility of such cooperative scheme and a significant coding gain is observed at data rate 12Mbps.

In this work we propose a new amplify-and-forward (AF) protocol and a new decode-and-forward (DF) protocol based on the Alamouti space-time (ST) code, chosen because of its decoding simplicity. We also apply a new selection criterion for AF and DF protocols that improves their performance and solves the problem of bad performance at low SNR. Finally, we apply the Alamouti AF and DF protocols to a "non-line-of-sight" (NLOS) scheme to bring diversity. Outage probabilities and simulation results show that at low spectral efficiency, in spite of their rate of 1/2 symbol per channel use, these Alamouti AF and DF protocols have better performance than the non-orthogonal AF (NAF) protocol.

In this work, we propose an amplify-and- forward (AF) protocol based on a new selection criterion, a function of the instantaneous capacities of all possible transmission schemes (with or without cooperation). The outage probability and the simulation results show that the new Adaptive AF protocol has better performance than the best known AF protocol (NAF). Moreover, this protocol solves the problem of the bad performance of NAF at low SNR. We also make a relay-selection to obtain a better diversity-order and then better performance.

We study the diversity of a Rayleigh product channel which is defined as a product of independent Rayleigh MIMO channels. More specifically, we obtain a closed-form expression of the diversity-multiplexing tradeoff (DMT) of a Rayleigh product channel with arbitrary dimensions and arbitrary number of product terms.

Summary form only given. In this paper, we consider multiantenna multihop relay channels in which the source signal arrives at the destination through N independent relaying hops in series. The main concern of this work is to design relaying strategies that efficiently utilize the relays in such a way that the diversity is maximized. First, we focus on the amplify-and-forward (AF) strategy with which the relays simply scale the received signal and retransmit it. More specifically, we characterize the diversity-multiplexing tradeoff (DMT) of the AF scheme in a general multihop channel with arbitrary number of antennas and arbitrary number of hops. The DMT is derived in closed-form expression as a function of the number of antennas at each node: as a first step, we provide some basic results on the DMT of the general Rayleigh product channels. It turns out that these results have very simple and intuitive interpretation. Then, the results are applied to the AF multihop channels which is shown to be equivalent to the Rayleigh product channel, in the DMT sense. Then, we mitigate the diversity suboptimality of the AF scheme via two kinds of partitions of the multihop channel : serial and parallel partitions. The serial partition corresponds to the intermediate decoding scheme. By supposing the relaying nodes could have full antenna cooperation, we study the fundamental problem that is when and where to decode to avoid diversity degradation. This scheme has minimum coding delay. The parallel partition corresponds to the distributed space-time processing. We establish conditions for the parallel partition to achieve the maximum diversity of the multihop channels. The parallel partition being rate-deficient in general, we propose a flip-and-forward (FF) scheme that achieves both the maximum diversity gain and multiplexing gain. The FF scheme is based on the parallel partition and works in a completely distributed manner. Coding schemes for both relaying strategies are proposed as well.

Downlink cooperation between base stations is a simple, efficient alternative to macrodiversity for providing QoS continuity during mobility in distributed cellular networks. It brings cooperation diversity and only requires data forwarding between base stations. This paper presents a strategy for downlink cooperation triggering, resource allocation and power control in an OFDMA-based system. Power control aims at maximizing the equivalent capacity that is achieved thanks to the diversity brought by relaying, while taking into account inter-cell interference. We use an iterative method which dedicates a proportion of the total power to relayed users. Simulation results show that our method increases capacity at any load. It importantly reduces the rejection probability thanks to SIR increase of users at cell's border. The paper also shows that cooperation should be limited to cell-border users for restricting additional resource consumption, and that it should make use of diversity as much as possible.

The full rate, full rank golden code showed to overcome all previous codes in (2 x 2) multiple input multiple output (MIMO) uncoded system when decoded with maximum- likelihood (ML) detectors. Therefore, its efficiency motivates us to study the code performance with suboptimal detectors, precisely two detectors based on decision feedback equalizer (DFE) detection. The first one is a DFE detector with preprocessing stage based minimum mean square error generalized DFE (MMSE-GDFE), Lattice reduction (LR) and Vertical-Bell Labs layered space-time (V-BLAST) greedy ordering. The second one is the enhanced maximum a posteriori DFE (E-MAP-DFE) detector. To extend the study for coded systems, other soft output algorithms are presented based on the first detection stage. The key idea of these algorithms is to provide candidate lists for more reliable detection. So, in this context, simulations were carried out to compare the detectors' performance.

In this paper, we propose for the first time a 2 × 2 space-time (ST) block code that can be applied with pulse position modulation (PPM) without introducing any constellation extension. This encoding scheme is adapted to low cost carrierless time-hopping ultra-wideband (TH-UWB) systems where information must be conveyed only by the time delay of the modulated signal that has a very low duty cycle. The proposed scheme permits to achieve full transmit diversity with M-ary PPM constellations for all values of M. Moreover, it permits to overcome the additional phase rotations or amplitude amplifications that are introduced by all the known ST codes such as the Alamouti code (S.M. Alamouti, 1998), the rate-1 codes proposed in B.A. Sethuraman et al. (2003), (A. J. Hammons and H. El Gamal, 2000) for PSK and the diversity schemes proposed in L. Yang and G.B. Giannakis (2004) for TH-UWB systems with PAM or PPM.

In cellular networks, base stations can cooperate in order to bring spatial diversity. Cooperative diversity enables to increase link capacity and signal to noise ratio. This paper presents source and relay base station's optimal power allocation in order to maximize the sum capacity over all relayed links. Average power allocation is solved by an iterative method which allocates relay and source powers separately, by convex optimization. Then source symbol powers are set with simple water-filling, in order to maximize the capacity. Simulation results show that sum capacity is highly increased by relaying under optimal power values. Relaying is especially efficient for user terminals who would have poor radio conditions without relaying. The paper also presents a simple method, based on path loss characterization, to determine the need for relaying. It can be used independently in the source base stations, which is particularly adapted for flat architectures.

A joint source-channel coding scheme for transmission of video over flat Rayleigh fading channels is described. The coding scheme consists of a spatiotemporal motion-compensated wavelet decomposition, a vector quantization of the coefficients through maximum-diversity lattices, and a linear labeling which minimizes simultaneously the source and channel distortion. Modulation diversity via rotated constellations produces the maximum-diversity lattices which increase robustness to channel fading without the addition of redundancy. Experimental results compare the proposed system to a prominent scalable video coder protected by more traditional convolutional codes, and superior performance is observed for high levels of channel noise.

In this work, we propose novel families of space-time (ST) block codes that can be associated with impulse radio ultra-wideband (IR-UWB) communication systems. The carrier-less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes. In fact, the last generation of complex-valued ST codes (namely, the perfect codes) cannot be associated with IR-UWB systems where the phase reconstitution at the receiver side is practically infeasible. On the other hand, while the perfect codes were considered mainly with quadrature amplitude modulation (QAM) and hexagonal (HEX) constellations, IR-UWB systems are often associated with pulse-position modulation (PPM) and hybrid PPM-PAM (pulse-amplitude modulation) constellations. In this paper, instead of adopting the classical approach of constructing ST codes over infinite fields or for the perfect codes), we study the possibility of constructing modulation-specific codes that are exclusive to PPM and PPM-PAM. The proposed full-rate codes are totally real, information lossless, and have a uniform average energy per transmit antenna. They permit to achieve a full diversity order with any number of transmit antennas. In some situations, the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real. Simulations performed over realistic indoor UWB channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras.

In this paper, we present a multidimensional trellis coded modulation scheme for a high rate 2times2 multiple-input multiple-output (MIMO) system over slow fading channels. Set partitioning of the Golden code is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions and Viterbi algorithm is applied for trellis decoding. In order to compute the branch metrics, a sphere decoder is used. The general framework for code design and optimization is given. Performance of the proposed scheme is evaluated by simulation and it is shown that it achieves significant performance gains over the uncoded Golden code

In this work, we extend the nonorthogonal amplify-and-forward (NAF) cooperative diversity scheme to the multiple-input multiple-output (MIMO) channel. A family of space-time block codes for a half-duplex MIMO NAF fading cooperative channel with N relays is constructed. The code construction is based on the nonvanishing determinant (NVD) criterion and is shown to achieve the optimal diversity-multiplexing tradeoff (DMT) of the channel. We provide a general explicit algebraic construction, followed by some examples. In particular, in the single-relay case, it is proved that the Golden code and the 4times4 Perfect code are optimal for the single-antenna and two-antenna cases, respectively. Simulation results reveal that a significant gain (up to 10 dB) can be obtained with the proposed codes, especially in the single-antenna case

In a slow-fading channel, how to find a cooperative diversity scheme that achieves the transmit diversity bound is still an open problem. In fact, all previously proposed amplify-and-forward (AF) and decode-and-forward (DF) schemes do not improve with the number of relays in terms of the diversity–multiplexing tradeoff (DMT) for multiplexing gains$r$higher than$0.5$. In this work, the class of slotted amplify-and-forward (SAF) schemes is studied. First, an upper bound on the DMT for any SAF scheme with an arbitrary number of relays$N$and number of slots$M$is established. Then, a sequential SAF scheme that can exploit the potential diversity gain in the high multiplexing gain regime is proposed. More precisely, in certain conditions, the sequential SAF scheme achieves the proposed DMT upper bound which tends to the transmit diversity bound when$M$goes to infinity. In particular, for the two-relay case, the three-slot sequential SAF scheme achieves the proposed upper bound and outperforms the two-relay nonorthorgonal amplify-and-forward (NAF) scheme of Azarianfor multiplexing gains$r\leq 2/3$. Numerical results reveal a significant gain of our scheme over the previously proposed AF schemes, especially in high spectral efficiency and large network size regime.

We construct a new family of space-time codes suited for multiple-antenna non-coherent communications over Rayleigh flat fading channels. These codes use all the complex degrees of freedom of the system, i.e. (M times(1-M/T)) symbols per channel use, where T is the code length and M is the number of transmit antennas. Their codewords belong to the Grassmann manifold GTldrM(C), the set of the M-dimensional vector subspaces of CT. Our codes are built from space-time codes for coherent systems via a non linear map (parameterization) called the exponential map. The relationships between some properties of the non-coherent space-time codes and their corresponding coherent codes are investigated. We also propose a simplified decoding for these classes of unitary space-time codes. We analyse the performance of these codes in terms of complexity and error probability and we compare them with some current best propositions, in particular training-based codes. The performance of our codes is substantially equivalent or slightly better than the one of training-based codes, under GLRT (Generalized Likelihood Ratio Test) decoding. When a simplified decoder is applied at the receiver, the error probability curves of the two propositions seem to be basically equivalent in the SIMO case with small block size, high spectral efficiency and high number of receive antennas, and in the 2times2 MIMO case with low spectral efficiency. In the other cases the training codes with simplified decoding seem to outperform our proposition.

In this paper, we consider the downlink of a space time block coded multiuser multiple-input multiple-output (MIMO) system. We propose a transmission scheme to support highest possible data rate and full diversity for multiuser MIMO systems. For this, threaded algebraic space-time block codes and perfect space-time block codes are employed. Different spreading matrices are used to separate the data streams of multiple users. After despreading the signal sequence at the receiver of each user, the maximum likelihood decoding is obtained by a lattice decoder. Performance of the multiuser MIMO system in the presence of multiple access interference is evaluated by simulations in terms of block error rate

This paper presents the construction of new totally-real space-time coding schemes suited for carrier-less ultra-wideband transmissions. These schemes are associated with pulse position modulation and with hybrid pulse amplitude and position modulation where the input data is modulated onto both the pulse amplitudes and positions. The new schemes have a uniform average transmitted energy per antenna and achieve full rate and full diversity with hybrid M-PPM-M'-PAM for all values of M' and for M ges 3, M ges 5 and {M = 5, M ges 7} with n = 2, 3 and 4 transmit antennas respectively

All previously proposed amplify-and-forward (AF) and decode-and-forward (DF) schemes do not improve with the number of relays in terms of the diversity-multiplexing tradeoff (DMT) for multiplexing gains r higher than 0.5. In this work, we study the class of slotted amplify-and-forward (SAF) schemes. We first establish an upper-bound on the DMT for any half-duplex SAF scheme with an arbitrary number of relays N and number of slots M. Then, we propose a naive SAF scheme that can exploit the potential diversity gain in the high multiplexing gain regime. More precisely, in certain conditions, the naive SAF scheme achieves the proposed DMT upper-bound which tends to the transmit diversity bound when M goes to infinity. In particular, for the two-relay case, the three-slot naive SAF scheme achieves the proposed upper-bound and outperforms the NAF scheme of Azarian et al. for multiplexing gains r les 2/3

The problem of designing space-time codes on the MIMO quasi-static channel have received considerable attention these last years. We now know how to design perfect space-time block codes, that is linear information preserving codes achieving the diversity-multiplexing gain (D-M) tradeoff (F. Oggier et al., 2004) (P. Elia et al., 2005). Recent standards using multiple antennas terminals such as IEEE 802.11n or IEEE 802.16e, for example, are based on OFDM. By using interleaving, such OFDM systems can be seen as parallel MIMO quasi-static channels. We propose, here, new perfect space-time block codes for parallel MIMO channels

In this paper, we present a new full rate scheme for exploiting diversity in multi-antenna ultra-wideband (UWB) systems. The independent data streams that are transmitted simultaneously from the different antennas are rendered orthogonal by the use of modified Hermite pulses. At a second time, appropriate real rotations enhance the transmit diversity level. We also consider, for the first time, the problem of maximum likelihood (ML) detection with multi-dimensional PPM and hybrid PPM-PAM constellations that can be used in conjunction with the proposed scheme

In this paper, we extend the amplify-and-forward (AF) cooperative diversity scheme to the context of impulse radio ultra wideband (IR-UWB). In particular, we apply a space-time (ST) coding scheme based on totally-real cyclic division algebras in order to achieve full diversity with no data rate losses. At a second time, the pulse repetitions are exploited in order to enhance the performance of the first scheme and to propose a new scheme that achieves comparable performance with lower complexity. These schemes are associated with pulse position modulation (PPM), pulse amplitude modulation (PAM) and hybrid pulse position and amplitude modulation (PPM-PAM)

In this paper, we propose a new MIMO-HSDPA transmission scheme with two transmit and two receive antennas, using an optimal Space-Time block code: the golden code. This code has a full rate, a full diversity, achieves the Diversity- Multiplexing gain tradeoff and preserves the mutual information. The proposed scheme is compared to the RCMPD a scheme which has also a full rate and a full diversity. The major disadvantage of the later is the generation of the multiple access interference (MAI) even on a flat fading channel. Simulation results show that the proposed scheme has better performances specially for high spectral efficiency. The RCMPD performance are hardly affected by the MAI.

A scalable video coder consisting of motion-compensated temporal filtering coupled with structured vector quantization plus a linear mapping of quantizer indexes that minimizes simultaneously source and channel distortions is presented. The linear index assignment takes the form of either a direct, uncoded mapping or a coded mapping via Reed-Muller codes. Experimental results compare the proposed system to a similar scheme using unstructured vector quantization as well as to a prominent scalable video coder protected by more traditional convolutional codes. The proposed system consistently outperforms the other two schemes by a significant margin for very noisy channel conditions.

In this paper, we present the construction of full-rate, fully diverse, and totally real space–time (ST) codes for ultra-wideband (UWB) transmissions. In particular, we construct two families of codes adapted to real carrierless UWB communications that employ pulse position modulation, pulse amplitude modulation, or a combination of the two. The first family encodes adjacent symbols and is constructed from totally real cyclic division algebras. The second family encodes the pulses used to convey one information symbol, and permits achieving high performance levels with reduced complexity. The first family of codes achieves only a fraction of the coding gain of the second one. Moreover, these coding gains are independent from the size of the transmitted constellation. For time-hopping multiple-access channels, the amplitude spreading code associated with the second family of codes is taken to be user-specific. In this case, a simple design criterion is proposed, and spreading matrices constructed according to this criterion permit reducing the level of multiple-access interference (MAI). Performance over realistic indoor UWB channels verify the theoretical claims, and show high performance levels and better immunity against MAI.

In this paper, we present the construction of full rate, fully diverse, and totally real space-time (ST) codes for ultra-wideband (UWB) transmissions. In particular, we construct two families of codes adapted to real carrierless UWB communications that employ pulse position modulation, pulse amplitude modulation, or a combination of the two. The first family encodes adjacent symbols and is constructed from totally real cyclic division algebras. The second family encodes the pulses used to convey one information symbol, and permits achieving high performance levels with reduced complexity. The first family of codes achieves only a fraction of the coding gain of the second one. Moreover, these coding gains are independent from the size of the transmitted constellation. For time-hopping multiple-access channels, the amplitude spreading code associated with the second family of codes is taken to be user-specific. In this case, a simple design criterion is proposed, and spreading matrices constructed according to this criterion permit reducing the level of multiple-access interference (MAI). Simulations performed over realistic indoor UWB channels verify the theoretical claims and show high performance levels and better immunity against MAI

In this paper, we introduce the notion of perfect space-time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas

A joint source-channel coding scheme of t + 2D decomposed video sequences and an iterative bit allocation are presented. The joint source-channel coding scheme consists of a vector quantization and a linear labelling by lattice constellations minimizing simultaneously the channel and the source distortion. The channel distortion, due to the linear labelling, is minimized and depends on the value of the noise variance and the variance of the source. The iterative algorithm results in an optimal codebook allocation subject to a global bit rate and a nonnegativity constraint. The overall flexible coding scheme is proved to be very efficient in noisy environments.

We consider multiple-antenna non-coherent communications over Rayleigh flat fading channels and single-antenna non-coherent systems with unknown channel phase. For both systems, we propose some sub-optimal simplified decodings for the class of unitary space-time codes obtained via the exponential map (I. Kammoun and J.-C. Belfiore, Nov. 2003). To this aim, we use the geometrical interpretation of these codes as sets of points over the Grassmann manifold G/sub TM/. We compare these codes with other propositions in the literature, for which a simplified decoder exists.

Joint source-channel coding of scalable video using motion-compensated temporal filtering is considered. The proposed coding scheme consists of a structured vector quantizer based on lattice constellations and a linear index assignment, which minimizes simultaneously the channel and source distortions. Both uncoded linear index assignment as well as partially coded linear index assignment via Reed-Muller codes are considered. The proposed system is compared to an unstructured quantizer with minimax index assignment. Simulation results indicate that, for a Gaussian channel, the structured-codebook scheme is very robust, maintaining near-noiseless performance even when the channel is very noisy. Additionally, the proposed structured-quantizer scheme outperforms its unstructured counterpart when channel noise levels are high.

The major contribution of this paper is the computation of an accurate approximation of the symbol error probability of multidimensional signal constellations used for transmission over independent Rayleigh fading channels. Here we attempt to compute the exact error probability and show how some apparently rather gross approximations still lead to an accurate result

In this paper, the Golden code for a 2/spl times/2 multiple-input multiple-output (MIMO) system is presented. This is a full-rate 2/spl times/2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+/spl radic/5/2.

We present a joint source-channel coding scheme developed for transmitting scalable video over a noisy channel. This scheme is based on a 2D+t motion-compensated wavelet decomposition of the video sequence, on a vector quantization and on an optimal linear labelling. In P. Knagenhjelm and E. Agrell's work (IEEE Trans. Information Theory, vol. IT 42, pp. 1139-1151, 1996), it is shown that on binary discrete channels, the channel distortion is minimized by linear labelling. In this paper, we provide a vector quantization method dependent on a linear labelling which minimizes not only the channel distortion but at the same time the distortion of our video source. Moreover, by exploiting a statistical model of the spatio-temporal wavelet coefficients we adapt the vector quantizer to the non-stationarity of the source. Simulation results demonstrate the robustness of this scheme under noisy channel conditions.

We investigate the performance of pilot-aided channel estimation and data detection for multi-input multi-output (MIMO) systems. We analyze and compare the Cramer-Rao bound (CRB) on channel tap estimation error for different design models of the pilot sequences. Then, the minimum mean square error (MMSE) estimation method with deflation is performed for channel identification for the embedded pilot scheme.

In this paper we present the Golden code for a 2times2 MIMO system. This is a full-rate 2times2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+radic5/2

We present a joint source-channel coding scheme developed for transmitting scalable video on a Rayleigh fading channel. Our scheme consists of a motion compensated temporal subband decomposition applied on groups of frames, followed by a spatial wavelet transform of the temporal subbands and a vector quantization. The vector quantization method is based on a linear labelling by "maximum component diversity" lattice constellations which minimizes not only the channel distortion but at the same time the distortion of our video source. These lattice constellations, which are multidimensional rotations generated from totally real cyclotomic fields, increase the diversity order on a Rayleigh fading channel. In addition, a rate-compatible punctured convolutional code in combination with a perfect interleaving is applied, providing even higher diversity.

We propose an algebraic framework for studying coherent space-time codes, based on arithmetic lattices on central simple algebras. For two transmit antennas, this algebra is called a quaternion algebra. For this reason, we call these lattices quaternionic lattices. The design criterion is the one described by V. Tarokh et al. (see IEEE Trans. Inf. Theory, vol.44, p.744-65, 1998).

Some M/spl times/T modulation matrices for M transmit antennas and T symbol periods, with M=2,3,4 and T=2, and M=T=4 are studied. A transmission rate of M symbols per channel use and a transmit diversity order of min(M,T) are achieved over a quasi-static fading channel when using rotated versions of a multidimensional quadratic amplitude modulation with spectral efficiency 2 bits/symbol. Extension to input constellations with higher spectral efficiencies is then considered. The modulations are then generalized to any number of transmit antennas M and any number of symbol periods T, such that a transmission rate of M symbols per channel use, and a transmit diversity of T are achieved under fast fading (ergodic scenario). By means of signal space diversity, the proposed modulations exploit the degrees of freedom of multiantenna channels and have moderate detection complexity at moderate and large signal-to-noise ratios (SNRs).

We construct a new family of linear space-time (ST) block codes by the combination of rotated constellations and the Hadamard transform, and we prove them to achieve the full transmit diversity over a quasi-static or fast fading channels. The proposed codes transmit at a normalized rate of 1 symbol/s. When the number of transmit antennas n=1, 2, or n is a multiple of four, we spread a rotated version of the information symbol vector by the Hadamard transform and send it over n transmit antennas and n time periods; for other values of n, we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n /spl times/ n ST code matrix. The codes maintain their rate, diversity, and coding gains for all real and complex constellations carved from the complex integers ring Z [i], and they outperform the codes from orthogonal design when using complex constellations for n > 2. The maximum-likelihood (ML) decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity. It is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity.

We construct a full data rate space-time (ST) block code over M=2 transmit antennas and T=2 symbol periods, and we prove that it achieves a transmit diversity of 2 over all constellations carved from Z[i]/sup 4/. Further, we optimize the coding gain of the proposed code and then compare it to the Alamouti code. It is shown that the new code outperforms the Alamouti (see IEEE J Select. Areas Commun., vol.16, p.1451-58, 1998) code at low and high signal-to-noise ratio (SNR) when the number of receive antennas N>1. The performance improvement is further enhanced when N or the size of the constellation increases. We relate the problem of ST diversity gain to algebraic number theory, and the coding gain optimization to the theory of simultaneous Diophantine approximation in the geometry of numbers. We find that the coding gain optimization is equivalent to finding irrational numbers "the furthest," from any simultaneous rational approximations.

We construct a full data rate space-time block code over M=2 transmit-antennas and T=2 symbol periods, and we prove it achieves a transmit diversity of 2 over all 4-dimensional constellations carved from the 4-dimensional ring of complex integers Z[i]/sup 4/. Further, we optimize the coding gain of our ST code and then compare it to the Alamouti scheme (see Alamouti, S.M., IEEE Journal Selec. Areas on Communications, vol.16, p.1451-8, 1998). For N>1, we prove that our code has a better performance than the Alamouti code. The performance improvement is further enhanced when N or the size of the constellation increases. We relate the problem of ST diversity gain to algebraic number theory, and the ST coding gain optimization to the theory of simultaneous Diophantine approximation in the geometry of numbers.

We present a generalized sphere decoding (GSD) algorithm and its application for detecting information symbols in the case where one has a system with more inputs (symbols) than outputs or the opposite situation. We study the special case of a multi-antenna scenario in a cellular system with N antennas at the mobile and M/spl ges/N antennas at the base station. GSD reaches the maximum likelihood (ML) performance for both up and down link with a moderate complexity.

A unified framework is presented in order to build lattice constellations matched to both the Rayleigh fading channel and the Gaussian channel. The method encompasses the situations where the interleaving is done on the real components or on two-dimensional signals. In the latter case, a simple construction of lattices congruent to the densest binary lattices with respect to the Euclidean distance is proposed. It generalizes, in a sense to be clarified later, the structural construction proposed by Forney (1991). These constellations are next combined with coset codes. The partitioning rules and the gain formula are similar to those used for the Gaussian channel.

Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. We present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. Some of these lattices also present a reasonable packing density and thus may be used at the same time over a Gaussian channel. Conversely, we show that particular versions of the best lattice packings (D/sub 4/, E/sub 6/, E/sub 8/, K/sub 12/, /spl Lambda//sub 16/, /spl Lambda//sub 24/), constructed from totally complex algebraic cyclotomic fields, present better performance over the Rayleigh fading channel. The practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links. Some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results.

We introduce a new technique for designing signal sets matched to the Rayleigh fading channel, In particular, we look for n-dimensional (n/spl ges/2) lattices whose structure provides nth-order diversity. Our approach is based on a geometric formulation of the design problem which in turn can be solved by using a number-geometric approach. Specifically, a suitable upper bound on the pairwise error probability makes the design problem tantamount to the determination of what is called a critical lattice of the body S={x=(x/sub 1/, /spl middot//spl middot//spl middot/, x/sub n/)/spl isin/R/sup n/, |/spl Pi//sub i=1//sup n/x/sub i/|/spl les/1}. The lattices among which we search for an optimal solution are the standard embeddings in R/sup n/ of the number ring of some totally real number field of degree n over Q. Simulation results confirm that this approach yields lattices with considerable coding gains.

We derive a Chernoff upper bound for the pairwise error probability in the presence of an additive white Gaussian noise and a Rayleigh or Rice correlated fading. The bound is useful for situations where perfect interleaving cannot be achieved. We use it to determine some indications in the design of optimum trellis coded modulation for correlated fading channels.>

The cutoff rate of Rician and Rayleigh channels characterized by time correlated fading is derived for M-ary phase shift keying (MPSK) modulation. It is useful for situations where perfect interleaving cannot be achieved. It indicates the practical achievable information rate of the channel when coding is employed. It is used to determine the potential coding gains of coded modulation over the correlated fading channel.>

The authors propose the design of a coded transmission system for the terrestrial urban radio channel, with a 4 bit-spectral efficiency. They evaluated the performances of a Reed-Solomon coded 64-QAM modulation on a Rayleigh fading channel. Three decoding algorithms are considered: a hard decision and an erasure Berlekamp-Massey decoding algorithm and a soft decision maximum likelihood decoding algorithm. By computing the cutoff rate they found that when the spectral efficiency is not close to 6, the gain of soft decision decoding over erasure decoding and the gain of erasure decoding over hard decision decoding are not so large. However, this gain must increase when the spectral efficiency becomes closer to 6 bits.>