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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An importance sampling algorithm for the Ising model with strong couplings
TL;DR: In this paper, the problem of estimating the partition function of the ferromagnetic Ising model in a consistent external magnetic field is addressed via importance sampling in the dual of the Forney factor graph representing the model.
Journal ArticleDOI
A concatenation scheme of LDPC codes and source codes for flash memories
TL;DR: A concatenation reliability scheme of LDPC codes and source codes, which aims to improve the performance ofLDPC codes for flash memories with stuck cells, and results verify that the proposed scheme outperforms the traditional scheme with only LDPC code.
Introduction to Forward-Error-Correcting Coding
TL;DR: This document is somewhere between a review and a how-to handbook, and considers "coding" to be only forward error correcting (FEC), as opposed to other uses of the term, which are source coding, encryption, spreading, etc.
Engineering Theory and Mathematics in the Early Development of Information Theory
TL;DR: It is shown that the contributions of American communications engineering theorists are directly tied to the socially constructed meanings of information theory held by members of the group and that the early advancement of information is linked to the mutual interactions between these two social groups.
References
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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.