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Information Theory, IEEE Transactions on

Issue 10 • Date Oct. 2008

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Displaying Results 1 - 25 of 35
  • Table of contents

    Page(s): C1 - C4
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    Freely Available from IEEE
  • IEEE Transactions on Information Theory publication information

    Page(s): C2
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    Freely Available from IEEE
  • On the Role of Estimate-and-Forward With Time Sharing in Cooperative Communication

    Page(s): 4409 - 4431
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1194 KB) |  | HTML iconHTML  

    In this paper, we focus on the general relay channel. We investigate the application of the estimate-and-forward (EAF) relaying scheme to different scenarios. Specifically, we study assignments of the auxiliary random variable that always satisfy the feasibility constraints. We then consider the Gaussian relay channel with coded modulation, where we show that a three-level quantization outperforms the Gaussian quantization commonly used to evaluate the achievable EAF rates in this scenario. Last, we consider the cooperative general broadcast scenario with a multistep conference between the receivers. We first apply EAF to obtain a general achievable rate region with a multistep conference. We then use an explicit assignment for the auxiliary random variables to obtain an explicit rate expression for the single common message case with a two-step conference. View full abstract»

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  • Mutual Information for Stochastic Signals and Fractional Brownian Motion

    Page(s): 4432 - 4438
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB) |  | HTML iconHTML  

    The mutual information between a stochastic signal and this signal plus a fractional Brownian motion (described as an additive fractional Gaussian noise channel) is expressed as the error of an estimation problem that can be naturally associated with this model. If the stochastic signal with the additive fractional Brownian motion occurs multiplied by a scalar parameter, then the rate of change of the mutual information with respect to this parameter is described by the error of another related estimation problem. These results generalize some results for a model where the fractional Brownian motion is a Brownian motion to a model with an arbitrary fractional Brownian motion. View full abstract»

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  • Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators

    Page(s): 4439 - 4447
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (326 KB) |  | HTML iconHTML  

    The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially tight analysis can be carried out by assessing the relevant moments of certain distance enumerators. The resulting bound has the following advantages: (i) it is at least as tight as Forney's bound, (ii) under certain symmetry conditions associated with the channel and the random coding distribution, it is simpler than Forney's bound in the sense that it involves an optimization over one parameter only (rather than two), and (iii) in certain special cases, like the binary symmetric channel (BSC), the optimum value of this parameter can be found in closed form, and so, there is no need to conduct a numerical search. We have not found yet a numerical example where this new bound is strictly better than Forney's bound and this may provide an additional evidence to support Forney's conjecture that his bound is tight for the average code. However, when applying the proposed analysis technique to a certain universal decoder with erasures, we demonstrate that it may yield significantly tighter exponential error bounds. We believe that this technique can be useful in simplifying and improving exponential error bounds in other problem settings as well. View full abstract»

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  • Cooperative Multiple-Access Encoding With States Available at One Transmitter

    Page(s): 4448 - 4469
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1044 KB) |  | HTML iconHTML  

    We generalize the Gel'fand-Pinsker model to encompass the setup of a memoryless multiple-access channel (MAC). According to this setup, only one of the encoders knows the state of the channel (noncausally), which is also unknown to the receiver. Two independent messages are transmitted: a common message and a message transmitted by the informed encoder. We find explicit characterizations of the capacity region with both noncausal and causal state information. Further, we study the noise-free binary case, and we also apply the general formula to the Gaussian case with noncausal channel state information, under an individual power constraint as well as a sum power constraint. In this case, the capacity region is achievable by a generalized writing-on-dirty-paper scheme. View full abstract»

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  • Dualities Between Entropy Functions and Network Codes

    Page(s): 4470 - 4487
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (450 KB) |  | HTML iconHTML  

    In communications networks, the capacity region of multisource network coding is given in terms of the set of entropy functions Gamma*. More broadly, determination of Gamma* would have an impact on converse theorems for multi-terminal problems in information theory. This paper provides several new dualities between entropy functions and network codes. Given a function g ges 0 defined on all subsets of N random variables, we provide a construction for a network multicast problem which is ldquosolvablerdquo if and only if g is the entropy function of a set of quasi-uniform random variables. The underlying network topology is fixed and the multicast problem depends on g only through link capacities and source rates. A corresponding duality is developed for linear network codes, where the constructed multicast problem is linearly solvable if and only if g is linear group characterizable. Relaxing the requirement that the domain of g be subsets of random variables, we obtain a similar duality between polymatroids and the linear programming bound. These duality results provide an alternative proof of the insufficiency of linear (and abelian) network codes, and demonstrate the utility of non-Shannon inequalities to tighten outer bounds on network coding capacity regions. View full abstract»

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  • List Decoding of Biorthogonal Codes and the Hadamard Transform With Linear Complexity

    Page(s): 4488 - 4492
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (214 KB) |  | HTML iconHTML  

    Let a biorthogonal Reed-Muller code RM (1,m) of length n = 2m be used on a memoryless channel with an input alphabet plusmn1 and a real-valued output R. Given any nonzero received vector y in the Euclidean space Rn and some parameter epsiisin(0,1), our goal is to perform list decoding of the code RM (1, m) and retrieve all codewords located within the angle arccos e from y. For an arbitrarily small epsi, we design an algorithm that outputs this list of codewords with the linear complexity order of n [ln2 isin] bit operations. Without loss of generality, let vector y be also scaled to the Euclidean length radic(n) of the transmitted vectors. Then an equivalent task is to retrieve all coefficients of the Hadamard transform of vector y whose absolute values exceed nisin. Thus, this decoding algorithm retrieves all ne-significant coefficients of the Hadamard transform with the linear complexity n [ln2 isin] instead of the complexity n In2n of the full Hadamard transform. View full abstract»

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  • Maximal Orders in the Design of Dense Space-Time Lattice Codes

    Page(s): 4493 - 4510
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (611 KB) |  | HTML iconHTML  

    In this paper, we construct explicit rate-one, full-diversity, geometrically dense matrix lattices with large, nonvanishing determinants (NVDs) for four transmit antenna multiple-input-single-output (MISO) space-time (ST) applications. The constructions are based on the theory of rings of algebraic integers and related subrings of the Hamiltonian quaternions and can be extended to a larger number of Tx antennas. The usage of ideals guarantees an NVD larger than one and an easy way to present the exact proofs for the minimum determinants. The idea of finding denser sublattices within a given division algebra is then generalized to a multiple-input-multiple-output (MIMO) case with an arbitrary number of Tx antennas by using the theory of cyclic division algebras (CDAs) and maximal orders. It is also shown that the explicit constructions in this paper all have a simple decoding method based on sphere decoding. Related to the decoding complexity, the notion of sensitivity is introduced, and experimental evidence indicating a connection between sensitivity, decoding complexity, and performance is provided. Simulations in a quasi-static Rayleigh fading channel show that our dense quaternionic constructions outperform both the earlier rectangular lattices and the rotated quasi-orthogonal ABBA lattice as well as the diagonal algebraic space-time (DAST) lattice. We also show that our quaternionic lattice is better than the DAST lattice in terms of the diversity-multiplexing gain tradeoff (DMT). View full abstract»

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  • Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

    Page(s): 4511 - 4527
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1341 KB) |  | HTML iconHTML  

    In this paper, a general criterion for space-time block codes (STBC) to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas [multiple-input-single-output (MISO)]. Particularly, the STBC with Toeplitz structure satisfies this criterion, and therefore, enables full diversity. Further examination of this Toeplitz STBC reveals the following important properties: (1) the symbol transmission rate can be made to approach unity; (2) applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant. In addition, if quadratic-amplitude modulation (QAM) is used as the signalling scheme, then for independent MISO flat-fading channels, the Toeplitz codes is proved to approach the optimal diversity-versus-multiplexing tradeoff with a zero-forcing (ZF) receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when maximum-likelihood (ML) detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pairwise error probability. View full abstract»

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  • Space–Time Block Codes Achieving Full Diversity With Linear Receivers

    Page(s): 4528 - 4547
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (692 KB) |  | HTML iconHTML  

    In most of the existing space-time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang-Liu-Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang-Liu-Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space-time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2times2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4. View full abstract»

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  • Decode-and-Forward Relaying With Quantized Channel State Feedback: An Outage Exponent Analysis

    Page(s): 4548 - 4564
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (628 KB) |  | HTML iconHTML  

    The problem of resource allocation to maximize the outage exponent over a fading relay channel using the decode-and-forward protocol with quantized channel state feedback (CSF) is studied. Three different scenarios are considered: relay-to-source, destination-to-relay, and destination-to-source-and-relay CSF. In the relay-to-source CSF scenario, it is found that using merely one bit of CSF to control the source transmit power is sufficient to achieve the multiantenna upper bound in a range of multiplexing gains. In the destination-to-relay CSF scenario, the systems slightly outperform dynamic decode-and-forward (DDF) at high multiplexing gains, even with only one bit of feedback. Finally, in the destination-to-source-and-relay CSF scenario, if the source-relay channel gain is unknown to the feedback quantizer at the destination, the diversity gain only grows linearly in the number of feedback levels, in sharp contrast to an exponential growth for multiantenna channels. In this last scenario, a simple scheme is shown to perform close to the corresponding upper bound. View full abstract»

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  • Rainbow Network Flow of Multiple Description Codes

    Page(s): 4565 - 4574
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (344 KB) |  | HTML iconHTML  

    This paper is an enquiry into the interaction between multiple description coding (MDC) and network routing. We are mainly concerned with rate-distortion optimized network flow of a multiple description (MD) source from multiple servers to multiple sinks. We aim at maximizing a collective metric of the quality of source reconstruction at all sinks, by optimally routing the MD source streams from the server nodes to the sinks. This problem turns out to be very different from conventional maximum network flow. The objective function involves not only the flow volume but also the diversity of the flow contents (i.e., distinction of descriptions), hence, the term rainbow network flow (RNF). For a general network topology, a general fidelity function, and an arbitrary distribution of MDC descriptions on the servers, we prove the RNF problem to be Max-SNP-hard. However, the problem becomes tractable in many practical scenarios, such as when MDC is balanced with descriptions of the same length and importance, when all source nodes have the complete set of MDC descriptions, and when the network topology is a tree or has only one sink. Polynomial-time RNF algorithms are developed for these cases. View full abstract»

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  • On the Complexity of Hardness Amplification

    Page(s): 4575 - 4586
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (375 KB) |  | HTML iconHTML  

    For deltaisin(0,1) and k,n isinN, we study the task of transforming a hard function f: {0,1}nrarr {0,1}, with which any small circuit disagrees on (1-delta)/2 fraction of the input, into a harder function f', with which any small circuit disagrees on (1-deltak)/2 fraction of the input. First, we show that such hardness amplification, when carried out in some black-box way, must require a high complexity. In particular, it cannot be realized by a circuit of depth d and size 2o(k 1/d) or by a nondeterministic circuit of size o(k/logk) (and arbitrary depth) for any deltaisin(0,1). This extends the result of Viola, which only works when (1-delta)/2 is small enough. Furthermore, we show that even without any restriction on the complexity of the amplification procedure, such a black-box hardness amplification must be inherently nonuniform in the following sense. To guarantee the hardness of the resulting function f', even against uniform machines, one has to start with a function f, which is hard against nonuniform algorithms with Omega(klog(1/delta)) bits of advice. This extends the result of Trevisan and Vadhan, which only addresses the case with (1-delta)/2=2- n. Finally, we derive similar lower bounds for any black-box construction of a pseudorandom generator (PRG) from a hard function. To prove our results, we link the task of hardness amplifications and PRG constructions, respectively, to some type of error-reduction codes, and then we establish lower bounds for such codes, which we hope could find interest in both coding theory and complexity theory. View full abstract»

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  • A Resource Framework for Quantum Shannon Theory

    Page(s): 4587 - 4618
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (692 KB) |  | HTML iconHTML  

    Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper, we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional, and memoryless. View full abstract»

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  • Second-Order Asymptotics in Fixed-Length Source Coding and Intrinsic Randomness

    Page(s): 4619 - 4637
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (473 KB) |  | HTML iconHTML  

    There is a difference between the optimal rates of fixed-length source coding and intrinsic randomness when we care about the second-order asymptotics. We prove this difference for general information sources and then investigate independent and identically distributed (i.i.d.) random variables and Markovian variables as examples. The difference is demonstrated through an investigation of the second-order asymptotic behavior of the rates. A universal fixed-length source code attaining the second-order optimal rate is also proposed. The difference between the rates of fixed-length source coding and intrinsic randomness proves that the outputs of fixed-length source codes are not uniformly distributed. View full abstract»

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  • Source Coding With Distortion Side Information

    Page(s): 4638 - 4665
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (858 KB) |  | HTML iconHTML  

    The impact of side information about the distortion measure in problems of quantization is analyzed. It is shown that such "distortion side information" is not only useful in general, but that in many cases knowing it at only the encoder is as good as knowing it at both encoder and decoder, and knowing it at only the decoder is useless. Moreover, it is shown that the strategy of exploiting distortion side information at the encoder by describing it for the decoder is inefficient. Thus, distortion side information is a natural complement to side information about the source signal, as studied by Wyner and Ziv, which if available only at the decoder is often as good as knowing it at both encoder and decoder. When both types of side information are present, conditions are established under which encoder-only distortion side information and decoder-only signal side information are sufficient in the high-resolution limit, and the rate penalty for deviating from this configuration is characterized. View full abstract»

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  • Successive Refinement for Hypothesis Testing and Lossless One-Helper Problem

    Page(s): 4666 - 4681
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (394 KB) |  | HTML iconHTML  

    We investigate two closely related successive refinement (SR) coding problems: 1) In the hypothesis testing (HT) problem, bivariate hypothesis H0:PXY against H1: PXPY, i.e., test against independence is considered. One remote sensor collects data stream X and sends summary information, constrained by SR coding rates, to a decision center which observes data stream Y directly. 2) In the one-helper (OH) problem, X and Y are encoded separately and the receiver seeks to reconstruct Y losslessly. Multiple levels of coding rates are allowed at the two sensors, and the transmissions are performed in an SR manner. We show that the SR-HT rate-error-exponent region and the SR-OH rate region can be reduced to essentially the same entropy characterization form. Single-letter solutions are thus provided in a unified fashion, and the connection between them is discussed. These problems are also related to the information bottleneck (IB) problem, and through this connection we provide a straightforward operational meaning for the IB method. Connection to the pattern recognition problem, the notion of successive refinability, and two specific sources are also discussed. A strong converse for the SR-HT problem is proved by generalizing the image size characterization method, which shows the optimal type-two error exponents under constant type-one error constraints are independent of the exact values of those constants. View full abstract»

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  • A Comment on the Weiss–Weinstein Bound for Constrained Parameter Sets

    Page(s): 4682 - 4684
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (137 KB) |  | HTML iconHTML  

    The Weiss-Weinstein bound (WWB) provides a lower limit on the mean-squared error (MSE) achievable by an estimator of an unknown random parameter. In this correspondence, it is shown that some previously proposed simplified versions of the bound do not always hold for constrained parameters, i.e., parameters whose distribution has finite support. These simplifications can produce results which are no longer lower bounds on the MSE. Sufficient conditions are provided for the reductions to be valid. View full abstract»

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  • Results of the Enumeration of Costas Arrays of Order 27

    Page(s): 4684 - 4687
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (245 KB) |  | HTML iconHTML  

    This correspondence presents the results of the enumeration of Costas arrays of order 27: all arrays found, except for one, are accounted for by the Golomb and Welch construction methods. View full abstract»

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  • On the Secrecy Capacity of Fading Channels

    Page(s): 4687 - 4698
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (762 KB) |  | HTML iconHTML  

    We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average signal-to-noise ratio (SNR) goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Overall, channel fading has a positive impact on the secrecy capacity and rate adaptation, based on the main channel CSI, is critical in facilitating secure communications over slow fading channels. View full abstract»

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  • Capacity Achieving LDPC Codes Through Puncturing

    Page(s): 4698 - 4706
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (367 KB) |  | HTML iconHTML  

    The performance of punctured low-definition parity-check (LDPC) codes under maximum-likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their average weight distributions (AWDs) and the corresponding asymptotic growth rate of the AWDs. In particular, it is proved that capacity-achieving codes of any rate and for any memoryless binary-input output-symmetric (MBIOS) channel under ML decoding can be constructed by puncturing some original LDPC code with small enough rate. Moreover, it is shown that the gap to capacity of all the punctured codes can be the same as the original code with a small enough rate. Conditions under which puncturing results in no rate loss with asymptotically high probability are also given in the process. These results show high potential for puncturing to be used in designing capacity-achieving codes, and in rate-compatible coding under any MBIOS channel. View full abstract»

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  • On the Achievable Rate Regions for Interference Channels With Degraded Message Sets

    Page(s): 4707 - 4712
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (353 KB) |  | HTML iconHTML  

    The interference channel with degraded message sets (IC-DMS) refers to a communication model, in which two senders attempt to communicate with their respective receivers simultaneously through a common medium, and one sender has complete and a priori (noncausal) knowledge about the message being transmitted by the other. A coding scheme that collectively has advantages of cooperative coding, collaborative coding, and dirty paper coding, is developed for such a channel. With resorting to this coding scheme, achievable rate regions of the IC-DMS in both discrete memoryless and Gaussian cases are derived. The derived achievable rate regions generally include several previously known rate regions as special cases. A numerical example for the Gaussian case further demonstrates that the derived achievable rate region offers considerable improvements over these existing results in the high-interference-gain regime. View full abstract»

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  • On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

    Page(s): 4712 - 4724
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1584 KB) |  | HTML iconHTML  

    The theory of multiple-input-multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input-single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beam- forming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback. View full abstract»

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  • Construction of Capacity Achieving (M, d, \infty ) Constrained Codes With Least Decoder Window Length

    Page(s): 4724 - 4726
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (119 KB) |  | HTML iconHTML  

    We present capacity achieving multilevel run-length-limited (ML-RLL) codes that can be decoded by a sliding window of size 2. 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.

Full Aims & Scope

Meet Our Editors

Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering