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Information Theory, IEEE Transactions on

Issue 12 • Date Dec. 2012

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Displaying Results 1 - 25 of 27
  • Table of Contents

    Publication Year: 2012 , Page(s): C1 - C4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2012 , Page(s): C2
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  • Computation of Universal Objects for Distributions Over Co-Trees

    Publication Year: 2012 , Page(s): 7021 - 7035
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3073 KB) |  | HTML iconHTML  

    For an ordered set, consider the model of distributions P for which an element that precedes another element is considered the more significant one in the sense that the implication abP(a) ≥ P(b) holds. It will be shown that if the ordered set is a finite co-tree, then the universal predictor for the model or, equivalently, the corresponding universal code, can be determined exactly via an algorithm of low complexity. Natural relations to problems on the computation of capacity and on the determination of information projections are established. More surprisingly, a direct connection to a problem of isotone regression also appears possible. View full abstract»

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  • A Linear Program for the Finite Block Length Converse of Polyanskiy–Poor–Verdú Via Nonsignaling Codes

    Publication Year: 2012 , Page(s): 7036 - 7044
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2984 KB) |  | HTML iconHTML  

    Motivated by recent work on entanglement-assisted codes for sending messages over classical channels, the larger, easily characterized class of nonsignaling codes is defined. Analyzing the optimal performance of these codes yields an alternative proof of the finite block length converse of Polyanskiy, Poor, and Verdú, and shows that they achieve this converse. This provides an explicit formulation of the converse as a linear program which has some useful features. For discrete memoryless channels, it is shown that nonsignaling codes attain the channel capacity with zero error probability if and only if the dispersion of the channel is zero. View full abstract»

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  • On the Equivalence Between Stein and De Bruijn Identities

    Publication Year: 2012 , Page(s): 7045 - 7067
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (8116 KB) |  | HTML iconHTML  

    This paper focuses on illustrating 1) the equivalence between Stein's identity and De Bruijn's identity, and 2) two extensions of De Bruijn's identity. First, it is shown that Stein's identity is equivalent to De Bruijn's identity under additive noise channels with specific conditions. Second, for arbitrary but fixed input and noise distributions under additive noise channels, the first derivative of the differential entropy is expressed by a function of the posterior mean, and the second derivative of the differential entropy is expressed in terms of a function of Fisher information. Several applications over a number of fields, such as signal processing and information theory, are presented to support the usefulness of the developed results in this paper. View full abstract»

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  • Upper Bounds of Error Probabilities for Stationary Gaussian Channels With Feedback

    Publication Year: 2012 , Page(s): 7068 - 7072
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1247 KB) |  | HTML iconHTML  

    In this paper, we discuss the coding schemes and error probabilities in information transmission over additive Gaussian noise channels with feedback, where the Gaussian noise processes are stationary but not necessarily white. In the case of the white Gaussian channel it is known that the minimum error probability, under the average power constraint, decreases faster than the exponential of any order. Recently Gallager and Nakiboğlu (2010) proposed a coding scheme for the white Gaussian channel and successfully showed the multiple-exponential decay of the error probability for all rates below capacity. This paper aims to prove that, without any special assumptions on the noise of the stationary Gaussian channel, the minimum error probability decreases multiple-exponentially fast. In general, no explicit formulas are known for the capacity of the stationary Gaussian channel. In this paper, we introduce a lower bound C* on the capacity C. Then we prove that the minimum error probability decreases multiple-exponentially fast for all rates below C*, but not for all rates below C. In the process of proving, the scheme proposed by Gallager and Nakiboğlu proves itself to be quite useful, even though the Gaussian channel is not white. View full abstract»

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  • The Degraded Poisson Wiretap Channel

    Publication Year: 2012 , Page(s): 7073 - 7085
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    Optical and near-optical band communication systems are known to be intrinsically more secure than comparable RF channels, due to their narrow beamwidths and, in some cases, their high atmospheric absorption. The use of coding against wiretapping for such channels is investigated. For the degraded Poisson wiretap channel model, the secrecy capacity is determined exactly. Moreover, a complete characterization of the rate-equivocation region is presented. For achievability, an optimal code is constructed explicitly by using a code designed by Wyner for the Poisson channel. The converse is proved in two ways: the first method leverages the low-SNR nature of the channel and relies only on simple properties of conditional expectation and classical information inequalities. The second method uses a link recently established between minimum mean square error estimation and mutual information over Poisson channels. View full abstract»

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  • PAC-Bayesian Inequalities for Martingales

    Publication Year: 2012 , Page(s): 7086 - 7093
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1640 KB) |  | HTML iconHTML  

    We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian (probably approximately correct) analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a martingale difference sequence shifted to the [0, 1] interval by the expectation of the same function of independent Bernoulli random variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality. View full abstract»

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  • Deinterleaving Finite Memory Processes Via Penalized Maximum Likelihood

    Publication Year: 2012 , Page(s): 7094 - 7109
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3858 KB) |  | HTML iconHTML  

    We study the problem of deinterleaving a set of finite-memory (Markov) processes over disjoint finite alphabets, which have been randomly interleaved by a finite-memory switch. The deinterleaver has access to a sample of the resulting interleaved process, but no knowledge of the number or structure of the component Markov processes, or of the switch. We study conditions for uniqueness of the interleaved representation of a process, showing that certain switch configurations, as well as memoryless component processes, can cause ambiguities in the representation. We show that a deinterleaving scheme based on minimizing a penalized maximum-likelihood cost function is strongly consistent, in the sense of reconstructing, almost surely as the observed sequence length tends to infinity, a set of component and switch Markov processes compatible with the original interleaved process. Furthermore, under certain conditions on the structure of the switch (including the special case of a memoryless switch), we show that the scheme recovers all possible interleaved representations of the original process. Experimental results are presented demonstrating that the proposed scheme performs well in practice, even for relatively short input samples. View full abstract»

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  • Analysis of a Collaborative Filter Based on Popularity Amongst Neighbors

    Publication Year: 2012 , Page(s): 7110 - 7134
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (7023 KB) |  | HTML iconHTML  

    In this paper, we analyze a collaborative filter that answers the simple question: What is popular amongst your “friends”? While this basic principle seems to be prevalent in many practical implementations, there does not appear to be much theoretical analysis of its performance. In this paper, we partly fill this gap. While recent works on this topic, such as the low-rank matrix completion literature, consider the probability of error in recovering the entire rating matrix, we consider probability of an error in an individual recommendation [bit error rate (BER)]. For a mathematical model introduced by Aditya et al. in 2009 and 2011, we identify three regimes of operation for our algorithm (named Popularity Amongst Friends) in the limit as the matrix size grows to infinity. In a regime characterized by large number of samples and small degrees of freedom (defined precisely for the model in the paper), the asymptotic BER is zero; in a regime characterized by large number of samples and large degrees of freedom, the asymptotic BER is bounded away from 0 and 1/2 (and is identified exactly except for a special case); and in a regime characterized by a small number of samples, the algorithm fails. We then compare these results with the performance of the optimal recommender. We also present numerical results for the MovieLens and Netflix datasets. We discuss the empirical performance in light of our theoretical results and compare with an approach based on low-rank matrix completion. View full abstract»

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  • Structure Theorems for Real-Time Variable Rate Coding With and Without Side Information

    Publication Year: 2012 , Page(s): 7135 - 7153
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5243 KB) |  | HTML iconHTML  

    The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate. Structure theorems, pertaining to the encoder and next-state functions, are derived for every given finite-state decoder, which can have access to side information. View full abstract»

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  • Approximately Optimal Wireless Broadcasting

    Publication Year: 2012 , Page(s): 7154 - 7167
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1572 KB) |  | HTML iconHTML  

    We study a wireless broadcast network, where a single source reliably communicates independent messages to multiple destinations, with the potential aid of relays and cooperation between destinations. The wireless nature of the medium is captured by the broadcast nature of transmissions as well as the superposition of transmitted signals plus independent Gaussian noise at the received signal at any radio. We propose a scheme that can achieve rate tuples within a constant gap away from the cut-set bound, where the constant is independent of channel coefficients and power constraints. First, for a deterministic broadcast network, we propose a new coding scheme, constructed by adopting a “receiver-centric” viewpoint, that uses quantize-and-forward relaying as an inner code concatenated with an outer Marton code for the induced deterministic broadcast channel. This scheme is shown to achieve the cut-set bound evaluated with product form distributions. This result is then lifted to the Gaussian network by using a deterministic network called the discrete superposition network as a formal quantization interface. This two-stage construction circumvents the difficulty involved in working with a vector nonlinear non-Gaussian broadcast channel that arises if we construct a similar scheme directly for the Gaussian network. View full abstract»

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  • The Diversity-Multiplexing Tradeoff of the MIMO Half-Duplex Relay Channel

    Publication Year: 2012 , Page(s): 7168 - 7187
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5317 KB) |  | HTML iconHTML  

    The fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel is characterized for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes. The key mathematical tool developed here that enables the explicit characterization of the diversity-multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random Wishart matrices. Besides being relevant here, this distribution result is interesting in its own right. Previously, without actually characterizing the diversity-multiplexing tradeoff, the optimality in this tradeoff metric of the dynamic compress-and-forward protocol based on the classical compress-and-forward scheme of Cover and El Gamal was shown by Yuksel and Erkip. However, this scheme requires global channel state information at the relay. In this paper, the so-called quantize-map and forward (QMF) coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the (channel dependent) switching time at the relay node. Moreover, in special classes of the MIMO half-duplex relay channel, the optimal tradeoff is shown to be attainable even without this knowledge. Such a result was previously known only for the half-duplex relay channel with a single antenna at each node, also via the QMF scheme. More generally, the explicit characterization of the tradeoff curve in this study enables the in-depth comparisons herein - f full-duplex versus half-duplex relaying as well as static versus dynamic relaying, both as a function of the numbers of antennas at the three nodes. View full abstract»

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  • The Generalized Degrees of Freedom Region of the MIMO Interference Channel and Its Achievability

    Publication Year: 2012 , Page(s): 7188 - 7203
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4688 KB) |  | HTML iconHTML  

    The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel (IC) is obtained for the general case of an arbitrary number of antennas at each node and where the signal-to-noise ratios (SNRs) and interference-to-noise ratios vary with arbitrary exponents to a nominal SNR. The GDoF-optimal coding scheme involves message splitting and partial interference decoding and consists of linear Gaussian superposition coding of the private and common submessages that can be seen as jointly performing signal-space and signal-level interference alignment. The admissible degree of freedom (DoF)-splits between the private and common messages are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime-where single-user DoF performance can be achieved simultaneously for both users-depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the single-input single-output case. For asymmetric numbers of antennas at the four nodes, the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain multiple-input multiple-output ICs it is a “V” curve. View full abstract»

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  • Signal Recovery on Incoherent Manifolds

    Publication Year: 2012 , Page(s): 7204 - 7214
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2378 KB) |  | HTML iconHTML  

    Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear submanifold of a high-dimensional ambient space. We introduce successive projections onto incoherent manifolds (SPIN), a first-order projected gradient method to recover the signal components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN significantly extends the scope of current recovery models and algorithms for low-dimensional linear inverse problems and matches (or exceeds) the current state of the art in terms of performance. View full abstract»

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  • On Optimum Parameter Modulation–Estimation From a Large Deviations Perspective

    Publication Year: 2012 , Page(s): 7215 - 7225
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2314 KB) |  | HTML iconHTML  

    We consider the problem of jointly optimum modulation and estimation of a real-valued random parameter, conveyed over an additive white Gaussian noise (AWGN) channel, where the performance metric is the large deviations behavior of the estimator, namely the exponential decay rate (as a function of the observation time) of the probability that the estimation error would exceed a certain threshold. Our basic result is in providing an exact characterization of the fastest achievable exponential decay rate, among all possible modulator-estimator (transmitter-receiver) pairs, where the modulator is limited only in the signal power, but not in bandwidth. This exponential rate turns out to be given by the reliability function of the AWGN channel. We also discuss several ways to achieve this optimum performance, and one of them is based on quantization of the parameter, followed by optimum channel coding and modulation, which gives rise to a separation-based transmitter, if one views this setting from the perspective of joint source-channel coding. This is in spite of the fact that, in general, when error exponents are considered, the source-channel separation theorem does not hold true. We also discuss several observations, modifications, and extensions of this result in several directions, including other channels, and the case of multidimensional parameter vectors. One of our findings concerning the latter is that there is an abrupt threshold effect in the dimensionality of the parameter vector: below a certain critical dimension, the probability of excess estimation error may still decay exponentially, but beyond this value, it must converge to unity. View full abstract»

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  • The Value of Feedback in Decentralized Detection

    Publication Year: 2012 , Page(s): 7226 - 7239
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3390 KB) |  | HTML iconHTML  

    We consider the decentralized binary hypothesis testing problem in networks with feedback, where some or all of the sensors have access to compressed summaries of other sensors' observations. We study certain two-message feedback architectures, in which every sensor sends two messages to a fusion center, with the second message based on full or partial knowledge of the first messages of the other sensors. We also study one-message feedback architectures, in which each sensor sends one message to a fusion center, with a group of sensors having full or partial knowledge of the messages from the sensors not in that group. Under either a Neyman-Pearson or a Bayesian formulation, we show that the asymptotically optimal (in the limit of a large number of sensors) detection performance (as quantified by error exponents) does not benefit from the feedback messages, if the fusion center remembers all sensor messages. However, feedback can improve the Bayesian detection performance in the one-message feedback architecture if the fusion center has limited memory; for that case, we determine the corresponding optimal error exponents. View full abstract»

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  • The Automorphism Group of a Self-Dual [72, 36, 16] Binary Code Does Not Contain Elements of Order 6

    Publication Year: 2012 , Page(s): 7240 - 7245
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2001 KB) |  | HTML iconHTML  

    The existence of an extremal code of length 72 is a long-standing open problem. Let C be a putative extremal code of length 72 and suppose that C has an automorphism g of order 6. We show that C, as an BBF2g〉 -module, is the direct sum of two modules; it is easy to determine one of them, while the other one has a very restrictive structure. We use this fact to do an exhaustive search and we do not find an extremal code. This proves that the automorphism group of an extremal code of length 72 does not contain elements of order 6. View full abstract»

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  • Classification of Poset-Block Spaces Admitting MacWilliams-Type Identity

    Publication Year: 2012 , Page(s): 7246 - 7252
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2388 KB) |  | HTML iconHTML  

    In this paper, we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical, and at any level of the poset, all the blocks have the same dimension. When the poset-block admits the MacWilliams-type identity, we explicitly state the relation between the weight enumerators of a code and its dual. View full abstract»

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  • The Weight Distributions of Cyclic Codes and Elliptic Curves

    Publication Year: 2012 , Page(s): 7253 - 7259
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2096 KB) |  | HTML iconHTML  

    Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes have been studied for many years and find many applications. The determination of the weight distributions of such codes is an open problem. Generally, the weight distributions of cyclic codes are difficult to determine. Utilizing a class of elliptic curves, this paper determines the weight distributions of dual codes of q-ary cyclic codes with two zeros for a few more cases, where q is an odd prime power. View full abstract»

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  • Message-Passing Algorithms and Improved LP Decoding

    Publication Year: 2012 , Page(s): 7260 - 7271
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3065 KB) |  | HTML iconHTML  

    Linear programming (LP) decoding for low-density parity-check codes (and related domains such as compressed sensing) has received increased attention over recent years because of its practical performance-coming close to that of iterative decoding algorithms-and its amenability to finite-blocklength analysis. Several works starting with the work of Feldman showed how to analyze LP decoding using properties of expander graphs. This line of analysis works for only low error rates, about a couple of orders of magnitude lower than the empirically observed performance. It is possible to do better for the case of random noise, as shown by Daskalakis and Koetter and Vontobel. Building on work of Koetter and Vontobel, we obtain a novel understanding of LP decoding, which allows us to establish a 0.05 fraction of correctable errors for rate-½ codes; this comes very close to the performance of iterative decoders and is significantly higher than the best previously noted correctable bit error rate for LP decoding. Our analysis exploits an explicit connection between LP decoding and message-passing algorithms and, unlike other techniques, directly works with the primal linear program. An interesting byproduct of our method is a notion of a “locally optimal” solution that we show to always be globally optimal (i.e., it is the nearest codeword). Such a solution can in fact be found in near-linear time by a “reweighted” version of the min-sum algorithm, obviating the need for LP. Our analysis implies, in particular, that this reweighted version of the min-sum decoder corrects up to a 0.05 fraction of errors. View full abstract»

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  • An Efficient Embedder for BCH Coding for Steganography

    Publication Year: 2012 , Page(s): 7272 - 7279
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1319 KB) |  | HTML iconHTML  

    This paper presents an improved data hiding technique based on BCH (n,k,t ) coding. The proposed embedder hides data into a block of input data by modifying some coefficients in the block in order to null the syndrome. The proposed embedder can hide data with less computational time and less storage capacity compared to the existing methods. The complexity of the proposed method is linear while that of other methods are exponential for any block size n. Thus, it is easy to extend this method to a large n. The BCH syndrome coding for steganography is now viable ascribed to the reduced complexity and its simplicity of the proposed embedder. View full abstract»

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  • Robust Distributed Storage of Residue Encoded Data

    Publication Year: 2012 , Page(s): 7280 - 7294
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5473 KB) |  | HTML iconHTML  

    We consider a problem where a physical quantity is repeatedly measured by replicated devices, yielding a stream of numerical data. Data are stored within the measuring devices and sporadically retrieved by a user. To avoid data losses due to large data streams with insufficient memory, the data are split into fragments, each of which is a compressed encoding of a number in the stream, and different fragments are stored in different, replicated devices. The devices are not allowed to communicate with each other, and they produce the local streams of fragments from independent measurements. Given the independence of measurements, the fragments are corrupted by independent errors, which are likely to be small integers, although errors of unbounded magnitude may also occur due to failures or to interferences. As devices may fail, or communication may be unreliable, the user may be unable to download fragments from some of the replicated devices, leading to fragment erasures. Our approach to the problem is to encode the data in a Residue Number System with Nonpairwise-Prime Moduli, named D-RNS-NPM. With n moduli and n residue digits, every replicated device is tied to a different modulus, with which it produces and stores a residue digit (i.e., a fragment) from the local measurement. Assuming an upper bound z, with z <; n, to the number of erasures, we show that the D-RNS-NPM guarantees the reconstruction of any number from a subset of at least n-z fragments. If fragments bear errors, whose magnitude is unrestricted for at most one error and upper bounded by a small δ for the others, reconstruction is within an approximation of ±δ, and this property is retained when errors cannot be detected due to the unbounded error multiplicity. The time complexity of the decoding algorithm is polynomial. This problem appears to be relevant in wireless sensor networks, and an application in this area is envi- ioned. View full abstract»

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  • Open Access

    Publication Year: 2012 , Page(s): 7295
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    Publication Year: 2012 , Page(s): 7296
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Aims & Scope

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

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Editor-in-Chief
Frank R. Kschischang

Department of Electrical and Computer Engineering