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Information Theory, IEEE Transactions on

Issue 6 • Date June 2011

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Displaying Results 1 - 25 of 71
  • Table of contents

    Publication Year: 2011 , Page(s): C1 - 3170
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2011 , Page(s): C2
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  • Operational Duality Between Lossy Compression and Channel Coding

    Publication Year: 2011 , Page(s): 3171 - 3179
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (278 KB) |  | HTML iconHTML  

    We explore the duality between lossy compression and channel coding in the operational sense: whether a capacity-achieving encoder-decoder sequence achieves the rate-distortion function of the dual problem when the channel decoder [encoder] is the source compressor [decompressor, resp.], and vice versa. We show that, if used as a lossy compressor, the maximum-likelihood channel decoder of a randomly chosen capacity-achieving codebook achieves the rate-distortion function almost surely. However, operational duality does not hold for every capacity achieving encoder-decoder sequence, or rate-distortion achieving compressor-decompressor sequence. We show that there exist optimal channel coding [lossy compression] schemes, which fail when used for the dual lossy compression [channel coding resp.] problem. View full abstract»

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  • Analog Matching of Colored Sources to Colored Channels

    Publication Year: 2011 , Page(s): 3180 - 3195
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (493 KB) |  | HTML iconHTML  

    Analog (uncoded) transmission provides a simple and robust scheme for communicating a Gaussian source over a Gaussian channel under the mean-squared-error (MSE) distortion measure. Unfortunately, its performance is usually inferior to the all-digital, separation-based source-channel coding solution, which requires exact knowledge of the channel at the encoder. The loss comes from the fact that except for very special cases, e.g., white source and channel of matching bandwidth (BW), it is impossible to achieve perfect matching of source to channel and channel to source by linear means. We show that by combining prediction and modulo-lattice operations, it is possible to match any colored Gaussian source to any colored Gaussian noise channel (of possibly different BW), hence achieve Shannon's optimum attainable performance R(D)=C. Furthermore, when the source and channel BWs are equal (but otherwise their spectra are arbitrary), this scheme is asymptotically robust in the sense that for high signal-to-noise ratio (SNR) a single encoder (independent of the noise variance) achieves the optimum performance. The derivation is based upon a recent modulo-lattice modulation scheme for transmitting a Wyner-Ziv source over a dirty-paper channel. View full abstract»

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  • Rate–Distortion Function via Minimum Mean Square Error Estimation

    Publication Year: 2011 , Page(s): 3196 - 3206
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    We derive a simple general parametric representation of the rate-distortion function of a memoryless source, where both the rate and the distortion are given by integrals whose integrands include the minimum mean square error (MMSE) of the distortion Δ = d(X, Y) based on the source symbol X, with respect to a certain joint distribution of these two random variables. At first glance, these relations may seem somewhat similar to the I-MMSE relations due to Guo, Shamai and Verdú, but they are, in fact, quite different. The new relations among rate, distortion, and MMSE are discussed from several aspects, and more importantly, it is demonstrated that they can sometimes be rather useful for obtaining non-trivial upper and lower bounds on the rate-distortion function, as well as for determining the exact asymptotic behavior for very low and for very large distortion. Analogous MMSE relations hold for channel capacity as well. View full abstract»

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  • Probability Estimation in the Rare-Events Regime

    Publication Year: 2011 , Page(s): 3207 - 3229
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (412 KB) |  | HTML iconHTML  

    We address the problem of estimating the probability of an observed string that is drawn i.i.d. from an unknown distribution. Motivated by models of natural language, we consider the regime in which the length of the observed string and the size of the underlying alphabet are comparably large. In this regime, the maximum likelihood distribution tends to overestimate the probability of the observed letters, so the Good-Turing probability estimator is typically used instead. We show that when used to estimate the sequence probability, the Good-Turing estimator is not consistent in this regime. We then introduce a novel sequence probability estimator that is consistent. This estimator also yields consistent estimators for other quantities of interest and a consistent universal classifier. View full abstract»

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  • On Pairs of f -Divergences and Their Joint Range

    Publication Year: 2011 , Page(s): 3230 - 3235
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (325 KB) |  | HTML iconHTML  

    We compare two f-divergences and prove that their joint range is the convex hull of the joint range for distributions supported on only two points. The proofs use various methods from topology and convex analysis. View full abstract»

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  • Finding the Maximizers of the Information Divergence From an Exponential Family

    Publication Year: 2011 , Page(s): 3236 - 3247
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (291 KB) |  | HTML iconHTML  

    This paper investigates maximizers of the information divergence from an exponential family ε. It is shown that the rI -projection of a maximizer P to ε is a convex combination of P and a probability measure P- with disjoint support and the same value of the sufficient statistics A. This observation can be used to transform the original problem of maximizing D(·∥ε) over the set of all probability measures into the maximization of a function D̅r over a convex subset of ker A. The global maximizers of both problems correspond to each other. Furthermore, finding all local maximizers of D̅r yields all local maximizers of D(·∥E). This paper also proposes two algorithms to find the maximizers of D̅r and applies them to two examples, where the maximizers of D(·∥ε) were not known before. View full abstract»

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  • Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing

    Publication Year: 2011 , Page(s): 3248 - 3259
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (281 KB) |  | HTML iconHTML  

    We investigate the role of directed information in portfolio theory, data compression, and statistics with causality constraints. In particular, we show that directed information is an upper bound on the increment in growth rates of optimal portfolios in a stock market due to causal side information. This upper bound is tight for gambling in a horse race, which is an extreme case of stock markets. Directed information also characterizes the value of causal side information in instantaneous compression and quantifies the benefit of causal inference in joint compression of two stochastic processes. In hypothesis testing, directed information evaluates the best error exponent for testing whether a random process Y causally influences another process X or not. These results lead to a natural interpretation of directed information I(YnXn) as the amount of information that a random sequence Yn = (Y1,Y2,..., Yn) causally provides about another random sequence Xn = (X1,X2,...,Xn). A new measure, directed lautum information, is also introduced and interpreted in portfolio theory, data compression, and hypothesis testing. View full abstract»

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  • The Discrete-Time Poisson Channel at Low Input Powers

    Publication Year: 2011 , Page(s): 3260 - 3272
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB) |  | HTML iconHTML  

    The asymptotic capacity at low input powers of an average-power limited or an average- and peak-power limited discrete-time Poisson channel is considered. For a Poisson channel whose dark current is zero or decays to zero linearly with its average input power ε, capacity scales like ε log 1/ε for small ε. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like ε log log 1/ε for small ε. View full abstract»

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  • Latent Capacity Region: A Case Study on Symmetric Broadcast With Common Messages

    Publication Year: 2011 , Page(s): 3273 - 3285
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3969 KB) |  | HTML iconHTML  

    We consider the problem of broadcast with common messages, and focus on the case that the common message rate RA, i.e., the rate of the message intended for all the receivers in the set A, is the same for all the set A of the same cardinality. Instead of attempting to characterize the capacity region of general broadcast channels, we only consider the structure of the capacity region that any broadcast channel should bear. The concept of latent capacity region is useful in capturing these underlying constraints, and we provide a complete characterization of the latent capacity region for the symmetric broadcast problem. The converse proof of this tight characterization relies on a deterministic broadcast channel model. The achievability proof generalizes the familiar rate transfer argument to include more involved erasure correction coding among messages, thus revealing an inherent connection between broadcast with common message and erasure correction codes. View full abstract»

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  • On the Degrees of Freedom of Finite State Compound Wireless Networks

    Publication Year: 2011 , Page(s): 3286 - 3308
    Cited by:  Papers (17)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (510 KB) |  | HTML iconHTML  

    We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multiple-input single-output (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weingarten have found inner and outer bounds on the DoF with 2 users. The bounds have a different character. While the inner bound collapses to unity as the number of states increases, the outer bound does not diminish with the increasing number of states beyond a threshold value. It has been conjectured that the outer bound is loose and the inner bound represents the actual DoF. In the complex setting (all signals, noise, and channel coefficients are complex variables), we solve a few cases to find that the outer bound - and not the inner bound - of Weingarten is tight. For the real setting (all signals, noise, and channel coefficients are real variables), we completely characterize the DoF, once again proving that the outer bound of Weingarten is tight. We also extend the results to arbitrary number of users. Second, we characterize the DoF of finite state scalar (single antenna nodes) compound X networks with arbitrary number of users in the real setting. Third, we characterize the DoF of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting. The key finding is that scalar interference networks and (real) X networks do not lose any DoF due to channel uncertainty at the transmitter in the finite state compound setting. The finite state compound MISO BC does lose DoF relative to the perfect CSIT scenario. However, what is lost is only the DoF benefit of joint processing at transmit antennas, without which the MISO BC reduces to an X network. View full abstract»

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  • A Distributed Numerical Approach to Interference Alignment and Applications to Wireless Interference Networks

    Publication Year: 2011 , Page(s): 3309 - 3322
    Cited by:  Papers (217)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (624 KB) |  | HTML iconHTML  

    Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work, we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory. View full abstract»

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  • Interference Alignment for Secrecy

    Publication Year: 2011 , Page(s): 3323 - 3332
    Cited by:  Papers (27)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (236 KB) |  | HTML iconHTML  

    This paper studies the frequency/time selective K-user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [(K-2)/(2K-2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [(K-2)/(2K)] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks. View full abstract»

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  • Communication by Energy Modulation: The Additive Exponential Noise Channel

    Publication Year: 2011 , Page(s): 3333 - 3351
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (618 KB) |  | HTML iconHTML  

    Communication across an additive exponential noise (AEN) channel is studied. The AEN channel is derived from a continuous-time Gaussian channel by assuming decoherence between the signal and noise components. Decoherence renders impossible the use of the complex amplitude and information is transmitted by modulating the signal energy. The AEN channel is shown to perform closely - in terms of channel, information rate, and error probability of binary codes, including the use of bit-interleaved coded modulation - to an equivalent discrete-time Gaussian channel of identical signal-to-noise ratio. Constellations are designed for low signal-to-noise ratios, where the minimum energy per bit is not universally attained by all modulations, and for high signal-to-noise ratios, where an equiprobable nonuniform constellation 0.76 dB away from capacity is described. The multiple-access AEN channel is also considered: its capacity region coincides with that of the Gaussian equivalent; feedback does not, however, enlarge the capacity region. View full abstract»

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  • Bits About the Channel: Multiround Protocols for Two-Way Fading Channels

    Publication Year: 2011 , Page(s): 3352 - 3370
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (427 KB) |  | HTML iconHTML  

    Most communication systems use some form of feedback, often related to channel state information. In this paper, we study diversity multiplexing tradeoff for both frequency division duplex (FDD) and time division duplex (TDD) systems, when both receiver and transmitter knowledge about the channel is noisy and potentially mismatched. For FDD systems, we first extend the achievable tradeoff region for 1.5 rounds of message passing to get higher diversity compared to the best known scheme, in the regime of higher multiplexing gains. We then break the mold of all current channel state based protocols by using multiple rounds of conferencing to extract more bits about the actual channel. This iterative refinement of the channel increases the diversity order with every round of communication. The protocols are on-demand in nature, using high powers for training and feedback only when the channel is in poor states. The key result is that the diversity multiplexing tradeoff with perfect training and K levels of perfect feedback can be achieved, even when there are errors in training the receiver and errors in the feedback link, with a multiround protocol which has K rounds of training and K-1 rounds of binary feedback. The above result can be viewed as a generalization of Zheng and Tse, and Aggarwal and Sabharwal, where the result was shown to hold for K=1 and K=2 , respectively. For TDD systems, we also develop new achievable strategies with multiple rounds of communication between the transmitter and the receiver, which use the reciprocity of the forward and the feedback channel. The multiround TDD protocol achieves a diversity-multiplexing tradeoff which uniformly dominates its FDD counterparts, where no channel reciprocity is available. View full abstract»

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  • On Optimal Power Control for Delay-Constrained Communication Over Fading Channels

    Publication Year: 2011 , Page(s): 3371 - 3389
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1396 KB) |  | HTML iconHTML  

    In this paper, the problem of optimal power control for delay-constrained communication over fading channels is studied. The objective is to find a power control law that optimizes the link layer performance, specifically, minimizes delay bound violation probability (or equivalently, the packet drop probability), subject to constraints on average power, arrival rate and delay bound. The transmission buffer size is assumed to be finite; hence, when the buffer is full, there will be packet drop. The fading channel under study has a continuous state, e.g., Rayleigh fading. Since directly solving the power control problem (which optimizes the link layer performance) is particularly challenging, the problem is decomposed into three subproblems and the three subproblems are solved iteratively; the resulting scheme is called joint queue length aware (JQLA) power control, which produces a local optimal solution to the three subproblems. It is proved that the solution that simultaneously solves the three subproblems is also an optimal solution to the optimal power control problem. Simulation results show that the JQLA scheme achieves superior performance over the time domain water filling and the truncated channel inversion power control. View full abstract»

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  • A Generalization of Nash Bargaining and Proportional Fairness to Log-Convex Utility Sets With Power Constraints

    Publication Year: 2011 , Page(s): 3390 - 3404
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (362 KB) |  | HTML iconHTML  

    Many solutions and concepts in resource allocation and game theory rely on the assumption of a convex utility set. In this paper, we show that the less restrictive assumption of a logarithmic “hidden” convexity is sometimes sufficient. We consider the problems of Nash bargaining and proportional fairness, which are closely related. We extend the Nash bargaining framework to a broader family of log-convex sets. We then focus on the set of feasible signal-to-interference-plus-noise ratios (SINRs), for the cases of individual power constraints and a sum power constraint. Under the assumption of log-convex interference functions, we show how Pareto optimality of boundary points depends on the interference coupling between the users. Finally, we provide necessary and sufficient conditions for strict log-convexity of the feasible SINR region. View full abstract»

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  • Theoretical Analysis on Bit Error Rate of VSG CDMA in Nakagami Fading

    Publication Year: 2011 , Page(s): 3405 - 3410
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (268 KB) |  | HTML iconHTML  

    In this paper, an efficient analytical technique for bit error rate (BER) of variable spreading gain code division multiple access (VSG CDMA) in Nakagami fading is introduced. Based on the accurate improve Gaussian approximation (IGA) technique, a new BER expression is derived in a closed form. Validated by Monte Carlo simulation, the proposed expression is used to accurately investigate the impacts of channel's conditions, power allocation and random users' distributions on the BER performance. View full abstract»

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  • On the Symbol Error Probability of Regular Polytopes

    Publication Year: 2011 , Page(s): 3411 - 3415
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (387 KB) |  | HTML iconHTML  

    An exact expression is derived for the symbol error probability when the vertices of the four-dimensional 24-cell are used for digital transmission in Gaussian noise. Corresponding expressions for other regular convex polytopes are summarized. Numerically stable versions of these error probabilities are also obtained. View full abstract»

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  • Large-System Analysis of Multiuser Detection With an Unknown Number of Users: A High-SNR Approach

    Publication Year: 2011 , Page(s): 3416 - 3428
    Cited by:  Papers (2)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (436 KB) |  | HTML iconHTML  

    We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service specified by error probability. View full abstract»

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  • Coset Codes for Compound Multiple Access Channels With Common Information

    Publication Year: 2011 , Page(s): 3429 - 3448
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (822 KB) |  | HTML iconHTML  

    Code construction is considered for arbitrary discrete memoryless compound multiple access channels (MACs) with common information. This class of channels includes MACs with/without common messages or with partially cooperating encoders. A construction method of code ensembles based on coset codes is proposed for these channels. Assuming joint maximum likelihood decoding, the performance of the proposed code ensemble is analyzed by deriving a lower bound on error exponents. A condition assuring that codes achieve the capacity region on average is given. It is seen that an elaborate combination of good linear codes gives capacity achieving codes for compound MACs with common messages or with partially cooperating encoders. The use of restricted ensembles with low-density parity check (LDPC) codes as component codes is also discussed. It is shown that a coset code ensemble based on nonbinary regular LDPC codes approaches the random coding exponent, and thus is capacity-achieving. View full abstract»

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  • Common Rate Support in Multi-Antenna Downlink Channels Using Semi-Orthogonal User Selection

    Publication Year: 2011 , Page(s): 3449 - 3461
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (922 KB) |  | HTML iconHTML  

    We consider a flat fading multiantenna downlink system with a large number of users where the objective is to deliver equal rates to nonoutage users with a low complexity. We show that in the limit of a large number of users, a zero-forcing beamforming strategy combined with a low complexity user grouping algorithm based on a semi-orthogonal user selection achieves asymptotically optimal performance, with respect to an upper bound that can be achieved when no interference is present among users. View full abstract»

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  • Slepian–Wolf Coding Over Cooperative Relay Networks

    Publication Year: 2011 , Page(s): 3462 - 3482
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (6320 KB) |  | HTML iconHTML  

    This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A Joint source-Wyner-Ziv encoding/sliding window decoding scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the submodular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks. View full abstract»

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  • Iterative Soft Joint Detection Algorithm for OFDM Systems

    Publication Year: 2011 , Page(s): 3483 - 3492
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (292 KB) |  | HTML iconHTML  

    In this paper, a novel iterative soft joint detection algorithm for orthogonal frequency division multiplexing (OFDM) systems is proposed. Without the need of channel estimation, it directly generates the a posteriori probabilities (APPs) of data symbols by very efficient computation. With the increase of iterations, the proposed algorithm gradually achieves near-optimal performance, while its complexity is only linear in the number of subcarriers. View full abstract»

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Aims & Scope

IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

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Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering