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Information Theory, IEEE Transactions on

Issue 10 • Date Oct. 2005

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Displaying Results 1 - 25 of 35
  • Table of contents

    Publication Year: 2005 , Page(s): c1 - c4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2005 , Page(s): c2
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  • Linear-time encodable/decodable codes with near-optimal rate

    Publication Year: 2005 , Page(s): 3393 - 3400
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (256 KB) |  | HTML iconHTML  

    We present an explicit construction of linear-time encodable and decodable codes of rate r which can correct a fraction (1-r-ε)/2 of errors over an alphabet of constant size depending only on ε, for every 00. The error-correction performance of these codes is optimal as seen by the Singleton bound (these are "near-MDS" codes). Such near-MDS linear-time codes were known for the decoding from erasures; our construction generalizes this to handle errors as well. Concatenating these codes with good, constant-sized binary codes gives a construction of linear-time binary codes which meet the Zyablov bound, and also the more general Blokh-Zyablov bound (by resorting to multilevel concatenation). Our work also yields linear-time encodable/decodable codes which match Forney's error exponent for concatenated codes for communication over the binary symmetric channel. The encoding/decoding complexity was quadratic in Forney's result, and Forney's bound has remained the best constructive error exponent for almost 40 years now. In summary, our results match the performance of the previously known explicit constructions of codes that had polynomial time encoding and decoding, but in addition have linear-time encoding and decoding algorithms. View full abstract»

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  • Lattices which are good for (almost) everything

    Publication Year: 2005 , Page(s): 3401 - 3416
    Cited by:  Papers (101)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (592 KB) |  | HTML iconHTML  

    We define an ensemble of lattices, and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings, sphere coverings, additive white Gaussian noise (AWGN) channel codes and mean-squared error (MSE) quantization codes. These lattices are generated by applying Construction A to a random linear code over a prime field of growing size, i.e., by "lifting" the code to Rn. View full abstract»

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  • A close-to-capacity dirty paper coding scheme

    Publication Year: 2005 , Page(s): 3417 - 3432
    Cited by:  Papers (111)  |  Patents (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (758 KB) |  | HTML iconHTML  

    The "writing on dirty paper"-channel model offers an information-theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter. It indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and thus dirty-paper coding may serve as a basic building block in both single-user and multiuser communication systems. We design an end-to-end coding realization of a system materializing a significant portion of the promised gains. We employ multidimensional quantization based on trellis shaping at the transmitter. Coset decoding is implemented at the receiver using "virtual bits." Combined with iterative decoding of capacity-approaching codes we achieve an improvement of 2dB over the best scalar quantization scheme. Code design is done using the EXIT chart technique. View full abstract»

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  • Sufficient conditions for existence of binary fix-free codes

    Publication Year: 2005 , Page(s): 3433 - 3444
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (360 KB) |  | HTML iconHTML  

    Two sufficient conditions are given for the existence of binary fix-free codes (i.e., both prefix-free and suffix-free). Let L be a finite multiset of positive integers whose Kraft sum is at most 3/4. It is shown that there exists a fix-free code whose codeword lengths are the elements of L if either of the following two conditions holds: i) The smallest integer in L is at least 2, and no integer in L, except possibly the largest one, occurs more than 2min(L)-2 times. ii) No integer in L, except possibly the largest one, occurs more than twice. The results move closer to the Ahlswede-Balkenhol-Khachatrian conjecture that Kraft sums of at most 3/4 suffice for the existence of fix-free codes. View full abstract»

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  • Sphere-packing bounds in the Grassmann and Stiefel manifolds

    Publication Year: 2005 , Page(s): 3445 - 3456
    Cited by:  Papers (29)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (388 KB) |  | HTML iconHTML  

    Applying the Riemann geometric machinery of volume estimates in terms of curvature, bounds for the minimal distance of packings/codes in the Grassmann and Stiefel manifolds will be derived and analyzed. In the context of space-time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length. This advocates large block lengths for the code design View full abstract»

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  • Generalized coset codes for distributed binning

    Publication Year: 2005 , Page(s): 3457 - 3474
    Cited by:  Papers (31)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (728 KB) |  | HTML iconHTML  

    In many multiterminal communication problems, constructions of good source codes involve finding distributed partitions (into bins) of a collection of quantizers associated with a group of source encoders. Further, computationally efficient procedures to index these bins are also required. In this work, we consider a constructive approach for distributed binning in an algebraic framework. Several application scenarios fall under the scope of this paper including the CEO problem, distributed source coding, and n-channel symmetric multiple description source coding with n>2. Specifically, in this exposition we consider the case of two codebooks while focusing on the Gaussian CEO problem with mean squared error reconstruction and with two symmetric observations. This problem deals with distributed encoding of correlated noisy observations of a source into descriptions such that the joint decoder having access to them can reconstruct the source with a fidelity criterion. We employ generalized coset codes constructed in a group-theoretic setting for this approach, and analyze the performance in terms of distance properties and decoding algorithms. View full abstract»

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  • Signature optimization for CDMA with limited feedback

    Publication Year: 2005 , Page(s): 3475 - 3492
    Cited by:  Papers (48)  |  Patents (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (616 KB) |  | HTML iconHTML  

    We study the performance of joint signature-receiver optimization for direct-sequence code-division multiple access (DS-CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a random vector quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent and identically distributed (i.i.d.) elements, we evaluate the received signal-to-interference plus noise ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear minimum mean-squared error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver, one feedback bit per signature coefficient achieves close to single-user performance. We also consider a less complex and suboptimal reduced-rank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalar-quantized and relayed to the transmitter. The large system performance of the quantized reduced-rank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference. View full abstract»

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  • Performance of linear reduced-rank multistage receivers for DS-CDMA in frequency-selective fading channels

    Publication Year: 2005 , Page(s): 3493 - 3517
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (825 KB) |  | HTML iconHTML  

    The performance of a set of linear reduced-rank multistage filter banks is studied in the context of multiuser detection for direct-sequence (DS) code-division multiple-access (CDMA) systems. The set of filter banks under consideration is comprised of the minimum mean-square error (MMSE), the minimum output energy (MOE), the best linear unbiased estimator (BLUE), and the maximum-likelihood (ML) detector. Based on a common framework for the multistage implementations of the aforementioned filter banks, the signal-to-interference plus noise ratios (SINRs) and bit-error rates (BERs) of these reduced-rank filter banks are studied for multipath Rayleigh-fading channels. A generic BER formula is provided for coherent detection and noncoherent differential detection schemes constructed under this common framework. Analysis shows that all of these performance measures are characterized by a kernel matrix Kmmse whose trace forms the output SINR of the MMSE filter bank. Through investigating the recursive structure of Kmmse, the output SINRs are proven to be monotonically increasing with the number of stages and upper-bounded by a number equal to the paths of the desired user's channel. The condition for asymptotically achieving this upper bound is also provided, which leads to the notion of effective user capacity of linear reduced-rank multiuser detection as well as serves as a test for the existence of a BER floor for coherent detection. In addition, the channel mismatch due to differential detection is also shown to yield a BER floor for noncoherent detection. Based on this analysis, a simple yet effective rule for choosing the number of stages is provided for both coherent and noncoherent linear multistage multiuser detection. View full abstract»

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  • Source-channel diversity for parallel channels

    Publication Year: 2005 , Page(s): 3518 - 3539
    Cited by:  Papers (76)  |  Patents (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (576 KB) |  | HTML iconHTML  

    We consider transmitting a source across a pair of independent, nonergodic channels with random states (e.g., slow-fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two commonly used source and channel encoding systems which correspond to exploiting diversity either at the physical layer through parallel channel coding or at the application layer through multiple description (MD) source coding. For on-off channel models, source coding diversity offers better performance. For channels with a continuous range of reception quality, we show the reverse is true. Specifically, we introduce a new figure of merit called the distortion exponent which measures how fast the average distortion decays with signal-to-noise ratio. For continuous-state models such as additive white Gaussian noise (AWGN) channels with multiplicative Rayleigh fading, optimal channel coding diversity at the physical layer is more efficient than source coding diversity at the application layer in that the former achieves a better distortion exponent. Finally, we consider a third decoding architecture: MD encoding with joint source-channel decoding. We show that this architecture achieves the same distortion exponent as systems with optimal channel coding diversity for continuous-state channels, and maintains the advantages of MD systems for on-off channels. Thus, the MD system with joint decoding achieves the best performance from among the three architectures considered, on both continuous-state and on-off channels. View full abstract»

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  • Transmitting to colocated users in wireless ad hoc and sensor networks

    Publication Year: 2005 , Page(s): 3540 - 3563
    Cited by:  Papers (32)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (640 KB) |  | HTML iconHTML  

    We consider wireless ad hoc networks and sensor networks where a remotely located source is transmitting information to a destined user embedded within a group of K densely packed physically colocated users enjoying favorable signal-to-noise ratio (SNR) conditions among themselves, but suffering from quasi-static flat Rayleigh fading with respect to the source. Stringent delay constraints require that information, once available, be transmitted immediately and delivered reliably to its destination during a period of one fading block, precluding waiting until the destined user enjoys favorable fading conditions with respect to the source. A cooperative transmission strategy is proposed for this scenario and its expected throughput is investigated. The strategy exhibits a substantial gain in throughput, especially when the colocation gain factor is high. In addition, a broadcast approach is incorporated into the transmission strategy suggesting further throughput benefits. View full abstract»

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  • Decentralized estimation in an inhomogeneous sensing environment

    Publication Year: 2005 , Page(s): 3564 - 3575
    Cited by:  Papers (104)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (364 KB) |  | HTML iconHTML  

    We consider decentralized estimation of a noise-corrupted deterministic parameter by a bandwidth-constrained sensor network with a fusion center. The sensor noises are assumed to be additive, zero mean, spatially uncorrelated, but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment. The classical best linear unbiased estimator (BLUE) linearly combines the real-valued sensor observations to minimize the mean square error (MSE). Unfortunately, such a scheme cannot be implemented in a practical bandwidth-constrained sensor network due to its requirement to transmit real-valued messages. In this paper, we construct a decentralized estimation scheme (DES) where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal-to-noise ratio (SNR). The resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter. The proposed DES is universal in the sense that each sensor compression scheme requires only the knowledge of local SNR, rather than the noise probability distribution functions (pdf), while the final fusion step is also independent of the local noise pdfs. We show that the MSE of the proposed DES is within a constant factor of 25/8 of that achieved by the classical centralized BLUE estimator. View full abstract»

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  • Equivalent models for queueing analysis of deterministic service time tree networks

    Publication Year: 2005 , Page(s): 3576 - 3584
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB) |  | HTML iconHTML  

    In this correspondence, we analyze feedforward tree networks of queues serving fixed-length packets. Using sample path conservation properties and stochastic coupling techniques, we analyze these systems without making any assumptions about the nature of the underlying input processes. In the case when the server rate is the same for all queues, the exact packet occupancy distribution in any queue of a multistage network is obtained in terms of a reduced two-stage equivalent model. Simple and exact expressions for occupancy mean and variance are derived from this result, and the network is shown to exhibit a natural traffic smoothing property, where preliminary stages act to smooth or improve traffic for downstream nodes. In the case of heterogeneous server rates, a similar type of smoothing is demonstrated, and upper bounds on the backlog distribution are derived. These bounds hold for general input streams and are tighter than currently known bounds for leaky bucket and stochastically bounded bursty traffic. View full abstract»

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  • On distances in uniformly random networks

    Publication Year: 2005 , Page(s): 3584 - 3586
    Cited by:  Papers (101)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (147 KB) |  | HTML iconHTML  

    The distribution of Euclidean distances in Poisson point processes is determined. The main result is the density function of the distance to the n-nearest neighbor of a homogeneous process in Ropfm, which is shown to be governed by a generalized Gamma distribution. The result has many implications for large wireless networks of randomly distributed nodes View full abstract»

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  • On the filtering problem for stationary random Z2-fields

    Publication Year: 2005 , Page(s): 3586 - 3593
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB) |  | HTML iconHTML  

    It is shown that whenever a stationary random field (Zn,m)n,m∈z is given by a Borel function f:Rz × Rz → R of two stationary processes (Xn)n∈z and (Ym)m∈z i.e., then (Zn, m) = (f((Xn+k)kεz, (Ym + ℓ )ℓ εz)) under a mild first coordinate univalence assumption on f, the process (Xn)n∈z is measurable with respect to (Zn,m)n,mεz whenever the process (Ym)m∈z is ergodic. The notion of universal filtering property of an ergodic stationary process is introduced, and then using ergodic theory methods it is shown that an ergodic stationary process has this property if and only if the centralizer of the dynamical system canonically associated with the process does not contain a nontrivial compact subgroup. View full abstract»

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  • A unified approach to linear estimation problems for nonstationary processes

    Publication Year: 2005 , Page(s): 3594 - 3601
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

    The linear least mean-square (LLMS) error estimation problem of a nonstationary signal corrupted by additive white noise is studied. The formulation of the problem is very general, in the sense that it deals with different estimation problems (smoothing, filtering, and prediction) involving correlation between the signal and the white noise and the possibility of estimating a linear operation (in quadratic mean) of the signal. The obtained solution is in the form of a suboptimum estimate and is derived by using the approximate series expansions for stochastic processes with the aim of solving the Wiener-Hopf equation in the general (nonstationary) case. The main characteristic of this new solution is that it can be computed efficiently using a recursive algorithm similar to the Kalman filter without requiring the signal to obey a state-space model. View full abstract»

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  • Recovery of exact sparse representations in the presence of bounded noise

    Publication Year: 2005 , Page(s): 3601 - 3608
    Cited by:  Papers (73)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (270 KB) |  | HTML iconHTML  

    The purpose of this contribution is to extend some recent results on sparse representations of signals in redundant bases developed in the noise-free case to the case of noisy observations. The type of question addressed so far is as follows: given an (n,m)-matrix A with m>n and a vector b=Axo, i.e., admitting a sparse representation xo, find a sufficient condition for b to have a unique sparsest representation. The answer is a bound on the number of nonzero entries in xo. We consider the case b=Axo+e where xo satisfies the sparsity conditions requested in the noise-free case and e is a vector of additive noise or modeling errors, and seek conditions under which xo can be recovered from b in a sense to be defined. The conditions we obtain relate the noise energy to the signal level as well as to a parameter of the quadratic program we use to recover the unknown sparsest representation. When the signal-to-noise ratio is large enough, all the components of the signal are still present when the noise is deleted; otherwise, the smallest components of the signal are themselves erased in a quite rational and predictable way View full abstract»

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  • Gaussian class multivariate Weibull distributions: theory and applications in fading channels

    Publication Year: 2005 , Page(s): 3608 - 3619
    Cited by:  Papers (74)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (536 KB) |  | HTML iconHTML  

    Ascertaining on the suitability of the Weibull distribution to model fading channels, a theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed. Novel analytical expressions for the joint probability density function (pdf), moment-generating function (mgf), and cumulative distribution function (cdf) are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers. Two specific distributions with arbitrary number of correlated variates are considered and studied: with exponential and with constant correlation where their pdfs are introduced. Both cases assume equal average fading powers, but not necessarily identical fading parameters. For the multivariate Weibull distribution with exponential correlation, useful corresponding formulas, as for the bivariate case, are derived. The presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection, equal-gain, and maximal-ratio combining (MRC) techniques operating over correlated Weibull fading channels. For these diversity receivers, several useful performance criteria such as the moments of the output signal-to-noise ratio (SNR) (including average output SNR and amount of fading) and outage probability are analytically derived. Moreover, the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach. The proposed mathematical analysis is complemented by various evaluation results, showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance. View full abstract»

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  • Antenna selection for unitary space-time modulation

    Publication Year: 2005 , Page(s): 3620 - 3631
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (676 KB) |  | HTML iconHTML  

    This correspondence studies receive antenna selection (AS) for multiple-antenna systems that employ unitary space-time (ST) signals, where the channel state information (CSI) is known neither at the transmitter nor at the receiver. Without CSI at the receiver, we perform AS only at the receiver and the selection is based on a maximum-norm criterion, i.e., a subset of receive antennas that have the largest received signal power is chosen. Using a Chernoff bound approach, we present theoretical performance analysis based on the pairwise error probability (PEP) and quantify the asymptotic performance at high signal-to-noise ratio (SNR) by giving the diversity and coding gain expressions. We prove that with no CSI at the receiver, the diversity gain with AS is preserved for unitary ST codes with full spatial diversity, the same as the case with known CSI. As a concrete example, for differential unitary ST modulation with M=2 transmit antennas and N=2 receive antennas, we have devised new excellent-performing parametric codes based on the derived PEP bound. The new codes, which are specifically designed for differential AS systems, outperform known differential codes when AS is employed. Corroborating simulations validate our analysis and code design. View full abstract»

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  • The collision channel with recovery

    Publication Year: 2005 , Page(s): 3631 - 3638
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB) |  | HTML iconHTML  

    We consider a simple conceptual model of random accessing to a receiver deploying multiuser detection techniques. The model is a simple extension of Massey and Mathys' collision channel without feedback in which a certain probability of recovery from collision is introduced. As the main result, we derive the slot-synchronized capacity region of this recovery channel and show that for sufficiently powerful multiuser detectors, maximal performance is achieved without any sophisticated transmission protocols. We also explore the effect of a simple fading model. View full abstract»

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  • On uniqueness Theorems for Tsallis entropy and Tsallis relative entropy

    Publication Year: 2005 , Page(s): 3638 - 3645
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (282 KB) |  | HTML iconHTML  

    The uniqueness theorem for Tsallis entropy was presented in H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783-1787, Aug. 2004 by introducing the generalized Shannon-Khinchin axiom. In the present correspondence, this result is generalized and simplified as follows: Generalization : The uniqueness theorem for Tsallis relative entropy is shown by means of the generalized Hobson's axiom. Simplification: The uniqueness theorem for Tsallis entropy is shown by means of the generalized Faddeev's axiom View full abstract»

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  • Low-density parity-check matrices for coding of correlated sources

    Publication Year: 2005 , Page(s): 3645 - 3654
    Cited by:  Papers (36)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (432 KB) |  | HTML iconHTML  

    Linear codes for a coding problem of correlated sources are considered. It is proved that we can construct codes by using low-density parity-check (LDPC) matrices with maximum-likelihood (or typical set) decoding. As applications of the above coding problem, a construction of codes is presented for multiple-access channel with correlated additive noises and a coding theorem of parity-check codes for general channels is proved. View full abstract»

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  • Some notes on the two-prime generator of order 2

    Publication Year: 2005 , Page(s): 3654 - 3657
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (184 KB) |  | HTML iconHTML  

    The two-prime generator of order 2 has several desirable randomness properties if the two primes are chosen properly. In particular, Ding deduced exact formulas for the (periodic) autocorrelation and the linear complexity of these sequences. In this note, we analyze parts of the period of the two-prime generator of order 2 and obtain bounds on the aperiodic autocorrelation and linear complexity profile. View full abstract»

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  • Properties of optimum binary message-passing decoders

    Publication Year: 2005 , Page(s): 3658 - 3665
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (368 KB) |  | HTML iconHTML  

    We consider a class of message-passing decoders for low-density parity-check (LDPC) codes whose messages are binary valued. We prove that if the channel is symmetric and all codewords are equally likely to be transmitted, an optimum decoding rule (in the sense of minimizing message error rate) should satisfy certain symmetry and isotropy conditions. Using this result, we prove that Gallager's Algorithm B achieves the optimum decoding threshold among all binary message-passing decoding algorithms for regular codes. For irregular codes, we argue that when the nodes of the message-passing decoder do not exploit knowledge of their decoding neighborhood, optimality of Gallager's Algorithm B is preserved. We also consider the problem of designing irregular LDPC codes and find a bound on the achievable rates with Gallager's Algorithm B. Using this bound, we study the case of low error-rate channels and analytically find good degree distributions for them. 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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Meet Our Editors

Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering