11,789 research outputs found

    Universal lossless source coding with the Burrows Wheeler transform

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    The Burrows Wheeler transform (1994) is a reversible sequence transformation used in a variety of practical lossless source-coding algorithms. In each, the BWT is followed by a lossless source code that attempts to exploit the natural ordering of the BWT coefficients. BWT-based compression schemes are widely touted as low-complexity algorithms giving lossless coding rates better than those of the Ziv-Lempel codes (commonly known as LZ'77 and LZ'78) and almost as good as those achieved by prediction by partial matching (PPM) algorithms. To date, the coding performance claims have been made primarily on the basis of experimental results. This work gives a theoretical evaluation of BWT-based coding. The main results of this theoretical evaluation include: (1) statistical characterizations of the BWT output on both finite strings and sequences of length n → ∞, (2) a variety of very simple new techniques for BWT-based lossless source coding, and (3) proofs of the universality and bounds on the rates of convergence of both new and existing BWT-based codes for finite-memory and stationary ergodic sources. The end result is a theoretical justification and validation of the experimentally derived conclusions: BWT-based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in Ziv-Lempel style codes and, for some BWT-based codes, within a constant factor of the optimal rate of convergence for finite-memory source

    Analysis of Alternative Metrics for the PAPR Problem in OFDM Transmission

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    The effective PAPR of the transmit signal is the standard metric to capture the effect of nonlinear distortion in OFDM transmission. A common rule of thumb is the log(N)(N) barrier where NN is the number of subcarriers which has been theoretically analyzed by many authors. Recently, new alternative metrics have been proposed in practice leading potentially to different system design rules which are theoretically analyzed in this paper. One of the main findings is that, most surprisingly, the log(N)(N) barrier turns out to be much too conservative: e.g. for the so-called amplifier-oriented metric the scaling is rather log⁥[log⁥(N)]\log[ \log(N)]. To prove this result, new upper bounds on the PAPR distribution for coded systems are presented as well as a theorem relating PAPR results to these alternative metrics.Comment: 5 pages, IEEE International Symposium on Information Theory (ISIT), 2011, accepted for publicatio

    Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data

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    We provide formal definitions and efficient secure techniques for - turning noisy information into keys usable for any cryptographic application, and, in particular, - reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a "fuzzy extractor" reliably extracts nearly uniform randomness R from its input; the extraction is error-tolerant in the sense that R will be the same even if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A "secure sketch" produces public information about its input w that does not reveal w, and yet allows exact recovery of w given another value that is close to w. Thus, it can be used to reliably reproduce error-prone biometric inputs without incurring the security risk inherent in storing them. We define the primitives to be both formally secure and versatile, generalizing much prior work. In addition, we provide nearly optimal constructions of both primitives for various measures of ``closeness'' of input data, such as Hamming distance, edit distance, and set difference.Comment: 47 pp., 3 figures. Prelim. version in Eurocrypt 2004, Springer LNCS 3027, pp. 523-540. Differences from version 3: minor edits for grammar, clarity, and typo

    Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units

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    We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever and Hinton, 2008; Le Roux and Bengio, 2008, 2010; Mont\'ufar and Ay, 2011) to units with arbitrary finite state spaces, and the vanishing approximation error to an arbitrary approximation error tolerance. For example, we show that a qq-ary deep belief network with L≄2+q⌈m−ή⌉−1q−1L\geq 2+\frac{q^{\lceil m-\delta \rceil}-1}{q-1} layers of width n≀m+log⁥q(m)+1n \leq m + \log_q(m) + 1 for some m∈Nm\in \mathbb{N} can approximate any probability distribution on {0,1,
,q−1}n\{0,1,\ldots,q-1\}^n without exceeding a Kullback-Leibler divergence of ÎŽ\delta. Our analysis covers discrete restricted Boltzmann machines and na\"ive Bayes models as special cases.Comment: 19 pages, 5 figures, 1 tabl

    Channel Coding at Low Capacity

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    Low-capacity scenarios have become increasingly important in the technology of the Internet of Things (IoT) and the next generation of mobile networks. Such scenarios require efficient and reliable transmission of information over channels with an extremely small capacity. Within these constraints, the performance of state-of-the-art coding techniques is far from optimal in terms of either rate or complexity. Moreover, the current non-asymptotic laws of optimal channel coding provide inaccurate predictions for coding in the low-capacity regime. In this paper, we provide the first comprehensive study of channel coding in the low-capacity regime. We will investigate the fundamental non-asymptotic limits for channel coding as well as challenges that must be overcome for efficient code design in low-capacity scenarios.Comment: 39 pages, 5 figure
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