Journal ArticleDOI
The theory of information and coding: A mathematical framework for communication
G. Longo
- Vol. 67, Iss: 10, pp 1467-1468
TLDR
The stochastic integral with respect to processes with values in a reflexive Banach space, Theor.Abstract:
14. M. Metivier, The stochastic integral with respect to processes with values in a reflexive Banach space, Theor. Probability 19 (1974), 758-787. 15. M. Metivier and G. Pistone, Une formule d'isométrie pour r intégrale stochastique Hilbertienne et équations d'évolution linéaires stochastiques, Z. Wahrscheinlicnkeitstheorie und Verw. Gebiete 33 (1975), 1-18. 16. P. A. Meyer, A decomposition theorem for supermartingales, Illinois J. Math. 6 (1962), 193-205. 17. , Intégrales stochastiques. IV, Lecture Notes in Math., vol. 39, Springer-Verlag, Berlin and New York, 1967, pp. 142-162. 18. , Un cours sur les intégrales stochastiques, Lecture Notes in Math., vol. 511, Springer-Verlag, Berlin and New York, 1976, pp. 245-400. 19. , Intégrales Hilbertiennes, Lecture Notes in Math., vol. 581, Springer-Verlag, Berlin and New York, 1977, pp. 446-461. 20. R. E. A. C. Paley, N. Wiener and A. Zygmund, Notes on random functions, Math. Z. 37 (1933), 647-668. 21. J. Pellaumail, Sur lintégrale stochastique et la décomposition de Doob-Meyer, Asterique 9 (1973), 1-125. 22. P. E. Protter, Markov solutions of stochastic differential equations, TL Wahrscheinlichkeitstheorie und Verw. Gebiete 41 (1977), 39-58. 23. , A comparison of stochastic integrals, Ann. Probability (to appear). 24. R. L. Stratonovich, A new representation for stochastic integrals and equations, SIAM. J. Control 4 (1966), 362-371. 25. N. Wiener, Differential-space, J. Math, and Physics 2 (1923), 131-174.read more
Citations
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Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Journal ArticleDOI
Good error-correcting codes based on very sparse matrices
TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.
Journal ArticleDOI
Vector quantization in speech coding
John Makhoul,S. Roucos,H. Gish +2 more
TL;DR: This tutorial review presents the basic concepts employed in vector quantization and gives a realistic assessment of its benefits and costs when compared to scalar quantization, and focuses primarily on the coding of speech signals and parameters.
Journal ArticleDOI
Finding the Number of Clusters in a Dataset
TL;DR: A simple, yet powerful nonparametric method for choosing the number of clusters based on distortion, a quantity that measures the average distance, per dimension, between each observation and its closest cluster center, is developed.
Journal ArticleDOI
On channel capacity per unit cost
TL;DR: It is shown that, if the input alphabet contains a zero-cost symbol, then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions.
References
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Dissertation
Optimal Information Storage: Nonsequential Sources and Neural Channels
TL;DR: This thesis studies the physical properties of a neural information storage channel and also the fundamental bounds on the storage of sources that have nonsequential semantics and formulate fidelity criteria that consider asymptotically large multisets and give conclusive, but trivialized, results in rate distortion theory.
Journal ArticleDOI
Cancer Classification With MicroRNA Expression Patterns Found By An Information Theory Approach
Yun Zheng,Chee Keong Kwoh +1 more
TL;DR: Find discriminatory miRNA patterns for cancer classification from miRNA expression profiles with an information theory approach and suggest that the expression patterns of these informative miRNAs are conserved in different vertebrates during the evolution process.
Journal ArticleDOI
Half-Duplex Relaying Over Slow Fading Channels Based on Quantize-and-Forward
TL;DR: It is shown that the QF scheme can significantly outperform the compress-and-forward scheme at finite signal-to-noise ratio (SNR) and it can achieve the optimal DMT at asymptotically high SNR and simple feedback from the destination node to the relay node can further improve the performance of theQF scheme.
Journal ArticleDOI
Dynamics of defects in the vector complex Ginzburg-Landau equation
TL;DR: In this article, a vector complex Ginzburg-Landau (CGL) equation is considered for the case of vector defects and a transition between different regimes of spatiotemporal dynamics is described.
Journal Article
The Quicksort algorithm and related topics
TL;DR: The time complexity of the Quicksort algorithm is studied and a complete demonstration of the variance of the number of comparisons required is provided, a known result but one whose detailed proof is not easy to read out of the literature.