We study the secrecy sum-rate (SSR) of a multi-user system in the presence of artificial noise (AN) and determine conditions under which it is necessary to add AN assuming eavesdropper (Eve) cannot remove the interference. We first derive a closed-form expression for the asymptotic SSR of the system and determine the optimum power allocation. The closed form expressions for the SSR and optimum power allocation closely match our simulation results. We also show that as the number of receive antennas at Eve increases, we need to allocate more power to AN in order to degrade reception at Eve.

We derive the asymptotic ergodic secrecy sum rate (ESSR) of block diagonalization precoding for physical-layer security in downlink multi-user wireless networks that use artificial noise. First, we derive the ESSR of the system. Then, we derive the power allocation and the asymptotic ESSR as the number of antennas increases. After, we derive an approximate expression for the optimum ratio of the number of transmit antennas to the number of receive antennas (Ψ). We then introduce the user dropping factor (UDF) as a means to derive the optimum number of users in the system under different scenarios and then derive the asymptotic optimum UDF, which gives the optimum number of scheduled users. We also study the effect of imperfect channel state information and derive a closed-form ESSR. Simulation results show that these precoders outperform channel inversion (CI) and regularized CI schemes in terms of the ESSR at all SNRs. We also show that as the number of receive antennas of each user increases, the asymptotic ESSR gap also increases.

We analyze asymptotic performance of regularized block diagonalization (RBD) precoding along with artificial noise (AN) used for physical layer security in downlink multi-user wireless networks. We derive the secrecy and asymptotic secrecy sum-rates for this scheme. We also derive closed form expressions for the asymptotic power allocation to the AN signal and legitimate users. Simulations show RBD precoding outperform regularized channel inversion (RCI) in terms of secrecy sum-rate with a margin of 0.5 bits/s/Hz.

We derive the asymptotic secrecy sum-rate of block diagonalization (BD) precoding for physical layer security in downlink multi-user wireless networks using artificial noise (AN). We first derive the secrecy sum-rate assuming that the channel of the eavesdropper is not known at the transmitter and then the asymptotic secrecy sum-rate is derived. The optimum power allocation for asymptotic secrecy sum-rate is derived after that. Simulation results show that the proposed precoders outperform channel inversion (CI) and regularized channel inversion (RCI) schemes in terms of the secrecy sum-rate at all SNRs. We also show that as the number of receive antennas of each user increases, the sum-rate gap between the proposed scheme and existing methods increases.

We develop a linearly constrained bimatrix game framework that can be used to model many practical problems in many disciplines, including jamming in packetized wireless networks. In contrast to the widely used zero-sum framework, in bimatrix games it is no longer required that the sum of the players' utilities be zero or constant, thus, ir can be used to model a much larger class of jamming problems. Additionally, in contrast to the standard bimatrix games, in linearly constrained bimatrix games, the players' strategies must satisfy some linear constraint/inequality, consequently, not all strategies are feasible and the existence of the Nash equilibrium (NE) is not guaranteed anymore. We provide the necessary and sufficient conditions under which the existence of the Nash equilibrium is guaranteed, and show that under linear constraints, the equilibrium pairs and the Nash equilibrium solution of the constrained game corresponds to the global maximum of a quadratic program. Finally, we use our game theoretic framework to find the optimal transmission and jamming strategies for a typical wireless link under power limited jamming.

We develop a constrained bimatrix game framework to model a packetized wireless communication link under jamming where the players' strategies must be chosen from some hyper-polyhedron defined by linear inequalities. In contrast to the widely used zero-sum framework, in bimatrix games it is no longer required that the sum of the players' payoffs to be zero (or a constant value). This allows us to model much larger class of jamming problems including scenarios where the players pursue different goals or have different views of the communication system. We provide the necessary and sufficient conditions under which the existence of the Nash equilibrium (NE) for the constrained bimatrix game is guaranteed. We study a typical jamming problem and show that the jammer can improve his payoff by switching from a zero-sum game to a bimatrix game.

We employ a game theoretic approach to formulate communication between two nodes over a wireless link in the presence of an adversary. We define a constrained, two-player, zero-sum game between a transmitter/receiver pair with adaptive transmission parameters and an adversary with average and maximum power constraints. In this model, the transmitter's goal is to maximize the achievable expected performance of the communication link, defined by a utility function, while the jammer's goal is to minimize the same utility function. Inspired by capacity/rate as a performance measure, we define a general utility function and a payoff matrix which may be applied to a variety of jamming problems. We show the existence of a threshold (JTH) such that if the jammer's average power exceeds JTH, the expected payoff of the transmitter at Nash Equilibrium (NE) is the same as the case when the jammer uses its maximum allowable power, Jmax, all the time. We provide analytical and numerical results for transmitter and jammer optimal strategies and a closed form expression for the expected value of the game at the NE. As a special case, we investigate the maximum achievable transmission rate of a rate-adaptive, packetized, wireless AWGN communication link under different jamming scenarios and show that randomization can significantly assist a smart jammer with limited average power.

We formulate the interaction between the communicating nodes and an adversary within a game-theoretic context. We show that earlier information-theoretic capacity results for a jammed channel correspond to a pure Nash Equilibrium (NE). However, when both players are allowed to randomize their actions (i.e., coding rate and jamming power) new mixed Nash equilibria appear with surprising properties. We show the existence of a threshold (JTH) such that if the jammer average power exceeds J TH, the channel capacity at the NE is the same as if the jammer was using its maximum allowable power, JMax, all the time. This indicates that randomization significantly advantages powerful jammers. We also show how the NE strategies can be derived, and we provide very simple (e.g., semi-uniform) approximations to the optimal communication and jamming strategies. Such strategies are very simple to implement in current hardware and software.

In many communications systems, data can be divided into different importance levels. For these systems, unequal error protection (UEP) techniques are used to guarantee lower BER for the more important classes. In particular, if the precise characteristics of the channel are not known, UEP can be used to recover the more important classes even in poor receiving conditions. In this paper, we derive bounds on the performance of unequal error protecting turbo codes. These bounds serve as an important tool in predicting the performance of these codes. In order to derive the bounds, we introduce the notion of UEP uniform interleaver which is a random interleaver that does not change the order of classes in the turbo code frame. We also present a method to derive the weight enumerating function for UEP turbo codes.

A novel Lattice Precoding scheme based on Eigenvalue decomposition (EDLP) is proposed for single user multiple- input multiple-output (MIMO) communication systems transmitting over slowly-varying flat-fading channels. This technique uses linear precoding to orthogonalize the channels, thus nullifying the interference. It employs a perturbation vector as well to reduce the transmitted power. The performance is enhanced by joint optimization of the linear precoder and the perturbation vector. As a result, the EDLP achieves not only full diversity order, but also significant power gain over comparable techniques. Although this structure enables EDLP to perform a global optimization on the closest lattice point search problem, the computational complexity of this nonlinear lattice precoding is comparable to linear techniques. Furthermore, the complexity at the receiver is kept constrained. When channel estimation errors are present, the proposed EDLP technique exhibits its robustness compared to other lattice precoding techniques.

A major concern in designing communication systems is to maintain quality of service for a wide range of channel conditions. This is an important issue particularly for the applications where precise characterization of the channel is impossible. For such applications, the source data can be classified into several classes and Unequal Error Protection (UEP) can be used to effectively protect the more important classes even in poor receiving conditions. This paper is focused on the study, design, and performance evaluation of unequal error protecting turbo coded modulation schemes. We first propose several schemes for unequal error protecting using turbo coded modulation. All these schemes provide high performance gains for more important classes that can hardly be achieved using conventional coded modulation schemes. We then study unequal error protecting turbo coded modulation schemes by deriving channel capacity and cutoff rates for different protection levels. We show that for more important classes more room is available for improvement.

A novel Coordinated Interference-aware Beamforming (CIB) technique for Multiple-Input-Multiple-Output (MIMO) Broadcast Channels (BC) is introduced. The CIB technique uses a method based on maximization of the Signal to Interference and Noise Ratio (SINR) at the front end of each receiver to balance the signal strength and the multi-user interference plus noise. This results in a closed form solution that can be used with any number of transmit and receive antennas. The resulting computational complexity is not more than well known non-iterative linear beamforming techniques. The new technique, even when equal power is assigned to each data stream, outperforms the sum rate achieved by the non-iterative linear beamforming techniques when employing waterfilling power allocation. Optimality of CIB is analyzed in some extreme cases of Signal to Noise Ratio (SNR) and the number of users. In contract to the intuition that Block Diagonalization Zero Forcing (BDZF) and other ZF techniques perform very well in large number of users since they are designed for canceling interuser interference, the sum rate of the proposed CIB grows faster than ZF. Additionally, the CIB provides more flexibility when employing further upper layer scheduling algorithms by supporting both diversity and spatial multiplexing for each user.

We present a new space-time block code (STBC) that is orthogonal, full rate and achieves full diversity for four transmit antennas when a special "triple-QPSK" modulation is used. The performance of this STBC is evaluated by Monte Carlo simulation and union bounding techniques. The pairwise error probability is presented. The analytical results match very well with the simulation results at reasonable signal to noise ratios (SNR). The performance of this STBC using the "triple-QPSK" is better than that of the conventional STBC.

We propose a new space-time block code for three transmit antennas using a special modulation scheme, called "twin QPSK". This space-time block code has rate one and achieves significant diversity gain that is close to full diversity when used with "twin QPSK" modulation. The decoder detects the transmitted symbols in pairs. The performance of this space- time block code is compared with the performance of other space-time block codes. It is observed that this code achieves better performance than conventional space-time block codes.

In this paper, performance of turbo trellis coded modulation (turbo-TCM) is investigated in the Gilbert-Elliot channel model. We consider three methods for transmission through this channel. In the first method no channel interleaver is used, in the second method we employ a channel symbol interleaver after the mapping to make the channel memoryless. Finally, in the last method a bit interleaver is used before mapping to increase to diversity. For all cases, we have assumed that the channel state is known at the receiver.

We analyze the performance of a fixed-point turbo decoder using two sliding window algorithms for the 3GPP standard. We show that the bit and frame error rate performance of the sliding window scheme strongly depends on the guard window size. Simulation results also indicate that small guard window sizes can significantly decrease the iteration gain for large frames.

This paper addresses the problem of low complexity iterative channel equalization in intersymbol interference channels using 8PSK modulation. In this paper, we apply a recently proposed low complexity iterative channel equalization technique, called the iterative decision feedback equalizer (IDFE) to a coded system using 8PSK modulation. In this system, the structure of the DFE has been modified to incorporate soft a priori information from previous iterations of the channel decoder in detection of the corrupted signal. As a result, in this algorithm complexity is only a linear function of channel memory length. Simulation results show that this technique, using a convolutional code with constraint length K=3 and interleaver size N=3000 over a known time invariant ISI channel achieves a remarkable gain of about 5 dB compared to the conventional DFE. Complexity evaluation also shows that the iterative DFE has advantages in terms of complexity compared to other types of turbo equalization techniques and is an appropriate candidate for EDGE (Enhanced Data rates for GSM Evolution) systems.

The performance of a turbo code with short block length depends critically on the interleaver design. There are two major criteria in the design of an interleaver: the distance spectrum of the code and the correlation between the information input data and the soft output of each decoder corresponding to its parity bits. This paper describes a new interleaver design for turbo codes with short block length based on these two criteria. A deterministic interleaver suitable for turbo codes is also described. Simulation results compare the new interleaver design to different existing interleavers.

We apply the standard union bound to turbo-coded modulation systems with maximum-likelihood decoding. To illustrate the methodology, we explicitly derive the bounds for the 2-bits/s/Hz 16 QAM system. Generalization of this bound to other turbo-coded modulation systems is straightforward. As in the case of the standard union bound for turbo codes, we expect these bounds to be useful for rather large values of signal-to-noise ratios, i.e., signal-to-noise ratios for which the code rate is smaller than the corresponding cutoff rate. The bound is based on "uniform interleaving" just as its counterpart for standard turbo coding. The derived bound provides a tool for comparing coded modulation schemes having different component codes, interleaver lengths, mappings, etc., using maximum-likelihood decoding. It is also useful in studying the effectiveness of various suboptimal decoding algorithms. The bounding technique is also applicable to other coded-modulation schemes such as serially concatenated coded modulation.

We derive performance bounds for turbo-coded modulation systems over fading channels. We consider a Ricean fading channel model both with and without channel-state information (CSI). This model obviously includes Rayleigh fading channel as a special case. The bounds are extensions of similar bounds derived for additive white Gaussian noise channels. For the special case of a Rayleigh fading channel with CSI, we also derive a tighter version of the bound. We illustrate the use of the new bounds via some numerical examples.

Multistage trellis-coded vector quantization (MS-TCVQ) is developed as a constrained trellis source-coding technique. The performance of the two-stage TCVQ is studied for Gaussian sources. Issues of stage-by-stage design, output alphabet selection, and complexity are addressed with emphasis on selecting and partitioning the stage codebooks. For a given rate, MS-TCVQ achieves low encoding and storage complexity compared to TCVQ, and comparisons with same-dimensional multistage vector quantization indicate a 0.5-3-dB improvement in signal-to-quantization-noise ratio.

We derive a new upper bound on the word- and bit-error probabilities of turbo codes with maximum-likelihood decoding by using the Gallager bound. Since the derivation of the bound for a given interleaver is intractable, we assume uniform interleaving as in the derivation of the standard union bound for turbo codes. The result is a generalization of the transfer function bound and remains useful for a wider range of signal-to-noise ratios, particularly for some range below the channel cutoff rate. The new bound is also applicable to other linear codes.

Optimal scalar quantizer design for transmission over a finite-state channel is considered. The objective Is to minimize the mean-squared error when the channel is in the normal mode of operation, while guaranteeing a minimum fidelity when the channel is in the "bad" state. An optimal quantizer design algorithm for the general case where noisy state information is available both at the receiver and at the transmitter is derived. It is shown that using mixed strategies is necessary in order to achieve the optimal performance. Finally, the case where the observation is noisy is considered and it is shown that the optimal scheme in this case is to apply the algorithm for the "no observation noise" to the mean-squared estimate of the desired random variable from the noisy data.

In this correspondence we consider the coding for multitrack magnetic recording systems. We provide analytical results related to uncoded and coded multitrack systems which constitute the basis of the code construction. We have designed matched spectral null codes for multitrack recording systems which give coding gains from 3 to 4.8 dB over uncoded systems.

Signal set expansion and set partitioning ideas from trellis coded modulation (TCM) have been previously applied to develop a source coding technique known as trellis coded quantization (TCQ). It has been also known that joint optimization of source and channel encoders/decoders results in substantial performance improvement. In this work, we investigate the performance of joint TCQ/TCM systems and develop various system optimization techniques. We consider channel optimized TCQ levels and asymmetric TCM symbol sets, and propose a simulated annealing based algorithm for joint optimization of TCQ levels and TCM symbols. Using these techniques signal to quantization noise ratio (SQNR) gains of 0.5-4 dB over nonoptimized systems are attained off-line. This, in turn, provides all the gain of going to a one step higher order trellis.

The error correcting capability of the unequal error protecting (UEP) Codes is described in terms of correcting errors in specific digits of a codeword even though other digits may be decoded incorrectly. We investigate the overall distortion when these codes are applied to transmission of analog sources in a communication system. Simulation and analytic results indicate the performance improvement gained by using UEP codes for various sources and source encoding structures.>

A K-out-of-M multiple-access channel is a mathematical model for transmission of information between a large number of potential transmitters and one receiver, where at any transmission interval only a (usually small) number of transmitters are actively transmitting their messages. We study the problem of matching between correlated information sources and a K-out-of-M multiple-access channel. We show that by employing the correlation between the information sources and using a two-step coding scheme better results can be achieved compared to separate source and channel coding. A coding and decoding scheme is described and sufficient conditions for reliable transmission of the correlated information sources via the K-out-of-M multiple-access channel, based on this scheme are obtained.>

Let\{(U_{i},V_{i})\}_{i=1}^{n}be a source of independent identically distributed (i.i.d.) discrete random variables with joint probability mass functionp(u,v)and common partw=f(u)=g(v)in the sense of Witsenhausen, Gacs, and Körner. It is shown that such a source can be sent with arbitrarily small probability of error over a multiple access channel (MAC)\{\cal X_{1} \times \cal X_{2},\cal Y,p(y|x_{1},x_{2})\},with allowed codes\{x_{l}(u), x_{2}(v)\}if there exist probability mass functionsp(s), p(x_{1}|s,u),p(x_{2}|s,v), such thatH(U|V)<I(X_{1}; Y|X_{2},V,S),H(V|U )<I(X_{2};Y|X_{1},U,S),H(U,V|W)<I(X_{1},X_{2};Y|W,S),H(U,V)