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Information Theory, IEEE Transactions on

Issue 10 • Date Oct. 2010

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  • Table of contents

    Publication Year: 2010 , Page(s): C1 - C4
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    Freely Available from IEEE
  • IEEE Transactions on Information Theory publication information

    Publication Year: 2010 , Page(s): C2
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  • DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models

    Publication Year: 2010 , Page(s): 4765 - 4780
    Cited by:  Papers (28)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (464 KB) |  | HTML iconHTML  

    This paper identifies the first general, explicit, and nonrandom MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in the rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding. View full abstract»

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  • Finite-SNR Diversity-Multiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems

    Publication Year: 2010 , Page(s): 4781 - 4792
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (356 KB) |  | HTML iconHTML  

    Diversity-multiplexing tradeoff (DMT) was characterized asymptotically (SNR- > infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse . The SNR-asymptotic DMT overestimates the finite-SNR one . This paper outlines a number of additional limitations and difficulties of the DMT framework and discusses their implications. Using the recent results on the size-asymptotic (in the number of antennas) outage capacity distribution, the finite-SNR, size-asymptotic DMT is derived for a broad class of fading distributions. The SNR range over which the finite-SNR DMT is accurately approximated by the SNR-asymptotic one is characterized. The multiplexing gain definition is shown to affect critically this range and thus should be carefully selected, so that the SNR-asymptotic DMT is an accurate approximation at realistic SNR values and thus has operational significance to be used as a design criterion. The finite-SNR diversity gain is shown to decrease with correlation and power imbalance in a broad class of fading channels, and such an effect is described in a compact, closed form. Complete characterization of the outage probability (or outage capacity) requires not only the finite-SNR DMT, but also the SNR offset, which is introduced and investigated as well. This offset, which is not accounted for in the DMT framework, is shown to have a significant impact on the outage probability for a broad class of fading channels, especially when the multiplexing gain is small. The analytical results and conclusions are validated via extensive Monte Carlo simulations. Overall, the size-asymptotic DMT represents a valuable alternative to the SNR-asymptotic one. View full abstract»

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  • Maximum Mutual Information Design for MIMO Systems With Imperfect Channel Knowledge

    Publication Year: 2010 , Page(s): 4793 - 4801
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (498 KB) |  | HTML iconHTML  

    New results on maximum mutual information design for multiple-input multiple-output (MIMO) systems are presented, assuming that both transmitter and receiver know only an estimate of the channel state as well as the transmit and receive correlation. Since an exact capacity expression is difficult to obtain for this case, a tight lower-bound on the mutual information between the input and the output of a MIMO channel has been previously formulated as a design criterion. However, in the previous literature, there has been no analytical expression of the optimum transmit covariance matrix for this lower-bound. Here it is shown that for the general case with channel correlation at both ends, there exists a unique and globally optimum transmit covariance matrix whose explicit expression can be conveniently determined. For the special case with transmit correlation only, the closed-form optimum transmit covariance matrix is presented. Interestingly, the optimal transmitters for the maximum mutual information design and the minimum total mean-square error design share the same structure, as they do in the case with perfect channel state information. Simulation results are provided to demonstrate the effects of channel estimation errors and channel correlation on the mutual information. View full abstract»

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  • Diversity Analysis and Design of Space–Time Multiblock Codes for MIMO Systems Equipped With Linear MMSE Receivers

    Publication Year: 2010 , Page(s): 4802 - 4819
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1073 KB) |  | HTML iconHTML  

    This paper addresses the problem of designing optimum full-symbol-rate linear space-time block codes (STBC) for a multi-input multi-output (MIMO) communication system with M transmitter and N ≥ M receiver antennas and a linear minimum mean square error (MMSE) receiver. By analyzing the detection error probability expression for the optimized STBC, it is shown that for QAM signaling, the maximum diversity gain for such a system is N - M + 1. The minimum probability of error STBC design is then extended to systems in which the transmission spans L independent realizations from a block fading channel model, and a (multiblock) linear MMSE receiver is employed. Necessary and sufficient conditions for the optimality of the code are obtained, and a systematic design method for generating codes that satisfy these conditions is presented. The detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed. It is proved that the error probability decreases with L, and it is shown numerically that the diversity gain increases with L. Thus, if the corresponding latency can be accommodated, for sufficiently large L an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block-fading channel and achieve higher diversity gain than that of any single-block system of the same symbol rate with a maximum likelihood (ML) receiver. The optimized multiblock linear system achieves this diversity at a substantially lower computational cost. In fact, the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver. View full abstract»

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  • On the Limitations of the Naive Lattice Decoding

    Publication Year: 2010 , Page(s): 4820 - 4826
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (255 KB) |  | HTML iconHTML  

    In this paper, the inherent drawbacks of the naive lattice decoding (NLD) for MIMO fading systems is investigated. We show that using the NLD for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the nonvanishing determinant property cannot achieve the optimal diversity-multiplexing tradeoff. Indeed, we show that in the case of NLD, when we fix the underlying lattice, all the codes based on full-rate lattices have the same diversity-multiplexing tradeoff as V-BLAST. Also, we derive a lower bound on the symbol error probability of the NLD for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the NLD has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding. View full abstract»

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  • Soft–Input Soft–Output Single Tree-Search Sphere Decoding

    Publication Year: 2010 , Page(s): 4827 - 4842
    Cited by:  Papers (39)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1241 KB) |  | HTML iconHTML  

    Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding. The computational complexity of SISO detection often poses significant challenges for practical receiver implementations, in particular in the context of multiple-input multiple-output (MIMO) wireless communication systems. In this paper, we present a low-complexity SISO sphere-decoding algorithm, based on the single tree-search paradigm proposed originally for soft-output MIMO detection in Studer (“Soft-output sphere decoding: Algorithms and VLSI implementation,” IEEE J. Sel. Areas Commun., vol. 26, no. 2, pp. 290-300, Feb. 2008). The new algorithm incorporates clipping of the extrinsic log-likelihood ratios (LLRs) into the tree-search, which results in significant complexity savings and allows to cover a large performance/complexity tradeoff region by adjusting a single parameter. Furthermore, we propose a new method for correcting approximate LLRs - resulting from sub-optimal detectors - which (often significantly) improves detection performance at low additional computational complexity. View full abstract»

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  • Why Does the Kronecker Model Result in Misleading Capacity Estimates?

    Publication Year: 2010 , Page(s): 4843 - 4864
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (913 KB) |  | HTML iconHTML  

    Many recent works that study the performance of multiple-input-multiple-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigenbases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this paper, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigenbases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low-and the high-SNR extremes: 1) sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low- SNR extreme, and 2) nonregularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme. View full abstract»

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  • Wideband Fading Channel Capacity With Training and Partial Feedback

    Publication Year: 2010 , Page(s): 4865 - 4873
    Cited by:  Papers (12)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (606 KB) |  | HTML iconHTML  

    We consider the capacity of a wideband fading channel with partial feedback, subject to an average power constraint. The channel is modeled as a set of parallel independent block Rayleigh fading subchannels with finite coherence time (L channel uses). The transmitter probes a subset of subchannels during each coherence time by transmitting pilot sequences for channel estimation. For each subchannel probed, one bit of feedback indicates whether or not the channel gain exceeds a threshold allowing transmission. Our problem is to optimize jointly the training (both length and power), number of subchannels probed (probing bandwidth), and feedback threshold to maximize the achievable rate (lower bound on ergodic capacity) taking into account the subchannel estimation error. Optimizing the probing bandwidth balances diversity against the quality of the subchannel estimate. We show that the achievable rate increases as S log L, where S is the signal-to-noise ratio, and exceeds the capacity with impulsive signaling (given by S) when L exceeds a (positive) threshold value. Moreover, the optimal probing bandwidth scales as SL/log2 L. In contrast, without feedback the optimal probing bandwidth for the probing scheme scales as SL1/3 and the achievable rate converges to S, where the gap diminishes as SL-1/3. View full abstract»

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  • Transmitter Waveform and Widely Linear Receiver Design: Noncooperative Games for Wireless Multiple-Access Networks

    Publication Year: 2010 , Page(s): 4874 - 4892
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1343 KB) |  | HTML iconHTML  

    The issue of noncooperative transceiver optimization in the uplink of a multiuser wireless code division multiple access data network with widely linear detection at the receiver is considered. While previous work in this area has focused on a simple real signal model, in this paper, a baseband complex representation of the data is used so as to properly take into account the I and Q components of the received signal. For the case in which the received signal is improper, a widely linear reception structure, processing separately the data and their complex conjugates, is considered. Several noncooperative resource allocation games are considered for this new scenario, and the performance gains granted by the use of widely linear detection are assessed through theoretical analysis. Numerical results confirm the validity of the theoretical findings and show that exploiting the improper nature of the data in noncooperative resource allocation brings remarkable performance improvements in multiuser wireless systems. View full abstract»

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  • Convergence of the Complex Envelope of Bandlimited OFDM Signals

    Publication Year: 2010 , Page(s): 4893 - 4904
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (273 KB) |  | HTML iconHTML  

    Orthogonal frequency division multiplexing (OFDM) systems have been used extensively in wireless communications in recent years; thus, there is significant interest in analyzing the properties of the transmitted signal in such systems. In particular, a large amount of work has focused on analyzing the variation of the complex envelope of the transmitted signal and on designing methods to minimize this variation. In this paper, it is established that the complex envelope of a bandlimited uncoded OFDM signal converges weakly to a Gaussian random process as the number of subcarriers goes to infinity. This shows that the properties of the OFDM signal will asymptotically approach those of a Gaussian random process over any finite time interval. The convergence proof is then extended to two important cases, namely, coded OFDM systems and systems with an unequal power allocation across subcarriers. View full abstract»

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  • Interior Point Decoding for Linear Vector Channels Based on Convex Optimization

    Publication Year: 2010 , Page(s): 4905 - 4921
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (682 KB) |  | HTML iconHTML  

    In the present paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, which is referred to hereinafter as interior point decoding, is designed for linear vector channels. The linear vector channels include several practically important channels, such as inter-symbol interference channels and partial response (PR) channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem. The proposed decoding algorithm is based on a numerical optimization technique known as the interior point method with barrier functions. Approximate variations of an interior point method based on the gradient descent and Newton methods are used to solve the relaxed MLD problem. Compared with a conventional joint message-passing decoder, from computer simulations, it is observed that the proposed decoding algorithm achieves better BER performance on PR channels with less decoding complexity in several cases. Furthermore, an extension of the proposed algorithm for high-order modulation formats, such as PAM and QAM, is presented. View full abstract»

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  • Joint Source Channel Coding With Side Information Using Hybrid Digital Analog Codes

    Publication Year: 2010 , Page(s): 4922 - 4940
    Cited by:  Papers (30)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (626 KB) |  | HTML iconHTML  

    We study the joint source-channel coding problem of transmitting a Gaussian source over a Gaussian channel in two cases: (i) the presence of interference known only to the transmitter and (ii) in the presence of side information about the source known only to the receiver. We introduce hybrid digital analog forms of the Costa and Wyner-Ziv coding schemes. We present the random coding counterpart of schemes based on lattices proposed by Kochman and Zamir. Then, we discuss applications of the hybrid digital analog schemes in the case of channel signal-to-noise ratio mismatch and for lossy multicasting of a common source with bandwidth compression. View full abstract»

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  • On Network Interference Management

    Publication Year: 2010 , Page(s): 4941 - 4955
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (282 KB) |  | HTML iconHTML  

    We study two building-block models of interference-limited wireless networks, motivated by the problem of joint Peer-to-Peer and Wide Area Network design. In the first case, a single “long-range” transmitter interferes with multiple parallel “short-range” transmissions, and, in the second case, multiple short-range transmitters interfere with a single long-range receiver. We identify the maximal degree-of-freedom region of the former network and show that multilevel superposition coding by the long-range transmitter performs optimally. Moreover, a simple power control strategy, performed by the long-range transmitter, achieves a region that is within one bit of the capacity region, under certain channel conditions. For the latter network, we show that short-range transmitter power control is degree-of-freedom optimal under certain channel conditions. View full abstract»

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  • Fundamental Limits of Wideband Localization— Part I: A General Framework

    Publication Year: 2010 , Page(s): 4956 - 4980
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1091 KB) |  | HTML iconHTML  

    The availability of position information is of great importance in many commercial, public safety, and military applications. The coming years will see the emergence of location-aware networks with submeter accuracy, relying on accurate range measurements provided by wide bandwidth transmissions. In this two-part paper, we determine the fundamental limits of localization accuracy of wideband wireless networks in harsh multipath environments. We first develop a general framework to characterize the localization accuracy of a given node here and then extend our analysis to cooperative location-aware networks in Part II. In this paper, we characterize localization accuracy in terms of a performance measure called the squared position error bound (SPEB), and introduce the notion of equivalent Fisher information (EFI) to derive the SPEB in a succinct expression. This methodology provides insights into the essence of the localization problem by unifying localization information from individual anchors and that from a priori knowledge of the agent's position in a canonical form. Our analysis begins with the received waveforms themselves rather than utilizing only the signal metrics extracted from these waveforms, such as time-of-arrival and received signal strength. Hence, our framework exploits all the information inherent in the received waveforms, and the resulting SPEB serves as a fundamental limit of localization accuracy. View full abstract»

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  • Fundamental Limits of Wideband Localization— Part II: Cooperative Networks

    Publication Year: 2010 , Page(s): 4981 - 5000
    Cited by:  Papers (104)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (849 KB) |  | HTML iconHTML  

    The availability of position information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information (EFI) for cooperative networks. This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy. Our results yield important insights into how and when cooperation is beneficial. View full abstract»

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  • Information Propagation Speed in Mobile and Delay Tolerant Networks

    Publication Year: 2010 , Page(s): 5001 - 5015
    Cited by:  Papers (21)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (552 KB) |  | HTML iconHTML  

    The goal of this paper is to increase our understanding of the fundamental performance limits of mobile and Delay Tolerant Networks (DTNs), where end-to-end multihop paths may not exist and communication routes may only be available through time and mobility. We use analytical tools to derive generic theoretical upper bounds for the information propagation speed in large scale mobile and intermittently connected networks. In other words, we upper-bound the optimal performance, in terms of delay, that can be achieved using any routing algorithm. We then show how our analysis can be applied to specific mobility models to obtain specific analytical estimates. In particular, in 2-D networks, when nodes move at a maximum speed v and their density is small (the network is sparse and asymptotically almost surely disconnected), we prove that the information propagation speed is upper bounded by (1 + O(v2))v in random waypoint-like models, while it is upper bounded by O(√vvv) for other mobility models (random walk, Brownian motion). We also present simulations that confirm the validity of the bounds in these scenarios. Finally, we generalize our results to 1-D and 3-D networks. View full abstract»

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  • Restricted Mobility Improves Delay-Throughput Tradeoffs in Mobile Ad Hoc Networks

    Publication Year: 2010 , Page(s): 5016 - 5029
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (504 KB) |  | HTML iconHTML  

    In this paper, we analyze asymptotic delay-throughput tradeoffs in mobile ad hoc networks comprising heterogeneous nodes with restricted mobility. We show that node spatial heterogeneity has the ability to drastically improve upon existing scaling laws established under the assumption that nodes are identical and uniformly visit the entire network area. In particular, we consider the situation in which each node moves around its own home-point according to a restricted mobility process which results into a spatial stationary distribution that decays as a power law of exponent δ with the distance from the home-point. For such restricted mobility model, we propose a novel class of scheduling and routing schemes, which significantly outperforms all delay-throughput results previously obtained in the case of identical nodes. In particular, for δ = 2 it is possible to achieve almost constant delay and almost constant per-node throughput (except for a polylogarithmic factor) as the number of nodes increases, even without resorting to sophisticated coding or signal processing techniques. View full abstract»

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  • Capacity Regions and Sum-Rate Capacities of Vector Gaussian Interference Channels

    Publication Year: 2010 , Page(s): 5030 - 5044
    Cited by:  Papers (35)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (307 KB) |  | HTML iconHTML  

    The capacity regions of vector, or multiple-input multiple-output, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sum-rate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels. View full abstract»

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  • General Classes of Performance Lower Bounds for Parameter Estimation—Part I: Non-Bayesian Bounds for Unbiased Estimators

    Publication Year: 2010 , Page(s): 5045 - 5063
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (529 KB) |  | HTML iconHTML  

    In this paper, a new class of lower bounds on the mean square error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by projecting each entry of the vector of estimation error on a Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform of the likelihood-ratio function. The integral transform generalizes the traditional derivative and sampling operators, which are applied on the likelihood-ratio function for computation of performance lower bounds, such as Cramér-Rao, Bhattacharyya, and McAulay-Seidman bounds. It is shown that some well-known lower bounds on the MSE of unbiased estimators can be derived from this class by modifying the kernel of the integral transform. A new lower bound is derived from the proposed class using the kernel of the Fourier transform. In comparison with other existing bounds, the proposed bound is computationally manageable and provides better prediction of the threshold region of the maximum-likelihood estimator, in the problem of single tone estimation. View full abstract»

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  • General Classes of Performance Lower Bounds for Parameter Estimation—Part II: Bayesian Bounds

    Publication Year: 2010 , Page(s): 5064 - 5082
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (525 KB) |  | HTML iconHTML  

    In this paper, a new class of Bayesian lower bounds is proposed. Derivation of the proposed class is performed via projection of each entry of the vector-function to be estimated on a Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform, applied on functions used for computation of bounds in the Weiss-Weinstein class. The integral transform generalizes the traditional derivative and sampling operators, used for computation of existing performance lower bounds, such as the Bayesian Cramér-Rao, Bayesian Bhattacharyya, and Weiss-Weinstein bounds. It is shown that some well-known Bayesian lower bounds can be derived from the proposed class by specific choice of the integral transform kernel. A new lower bound is derived from the proposed class using the Fourier transform kernel. The proposed bound is compared with other existing bounds in terms of signal-to-noise ratio (SNR) threshold region prediction in the problem of frequency estimation. The bound is shown to be computationally manageable and provides better prediction of the SNR threshold region, exhibited by the maximum a posteriori probability (MAP) and minimum-mean-square-error (MMSE) estimators. View full abstract»

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  • A State-Space Approach to Optimal Level-Crossing Prediction for Linear Gaussian Processes

    Publication Year: 2010 , Page(s): 5083 - 5096
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (979 KB) |  | HTML iconHTML  

    In this paper, approximations of an optimal level-crossing predictor for a zero-mean stationary linear dynamical system driven by Gaussian noise in state-space form are investigated. The study of this problem is motivated by the practical implications for design of an optimal alarm system, which will elicit the fewest false alarms for a fixed detection probability in this context. This work introduces the use of Kalman filtering in tandem with the optimal level-crossing prediction problem. It is shown that there is a negligible loss in overall accuracy when using approximations to the theoretically optimal predictor, at the advantage of greatly reduced computational complexity. View full abstract»

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  • The Golden Ratio Encoder

    Publication Year: 2010 , Page(s): 5097 - 5110
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (429 KB) |  | HTML iconHTML  

    This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder with β = φ = (1 + √5)/2, the golden ratio. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. Furthermore, a formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is proposed. View full abstract»

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  • Information Theoretic Bounds for Compressed Sensing

    Publication Year: 2010 , Page(s): 5111 - 5130
    Cited by:  Papers (48)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (548 KB) |  | HTML iconHTML  

    In this paper, we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input noise models where the noise enters before the projection. We consider two types of distortion for reconstruction: support errors and mean-squared errors. Our goal is to relate the number of measurements, m , and SNR, to signal sparsity, k, distortion level, d, and signal dimension, n . We consider support errors in a worst-case setting. We employ different variations of Fano's inequality to derive necessary conditions on the number of measurements and SNR required for exact reconstruction. To derive sufficient conditions, we develop new insights on max-likelihood analysis based on a novel superposition property. In particular, this property implies that small support errors are the dominant error events. Consequently, our ML analysis does not suffer the conservatism of the union bound and leads to a tighter analysis of max-likelihood. These results provide order-wise tight bounds. For output noise models, we show that asymptotically an SNR of ((n)) together with (k (n/k)) measurements is necessary and sufficient for exact support recovery. Furthermore, if a small fraction of support errors can be tolerated, a constant SNR turns out to be sufficient in the linear sparsity regime. In contrast for input noise models, we show that support recovery fails if the number of measurements scales as o(n(n)/SNR), implying poor compression performance for such cases. Motivated by the fact that the worst-case setup requires significantly high SNR and substantial number of measurements for input and output noise models, we consider a Bayesian setup. To derive necessary conditions, we develop novel extensions to Fano's inequality to handle continuous domains and arbitrary distortions. We then develop a new max-likelihood analysis over the set - - of rate distortion quantization points to characterize tradeoffs between mean-squared distortion and the number of measurements using rate-distortion theory. We show that with constant SNR the number of measurements scales linearly with the rate-distortion function of the sparse phenomena. View full abstract»

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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