论文信息 - Distributions and expectations of singular random variables

Distributions and expectations of singular random variables

Intersymbol and cochannel interference in a communications channel can often be modelled as the sum of an infinite series of random variables with weights which decay fairly rapidly. Frequently, this yields a random variable which is singular but non-atomic. The Hausdorff dimension of the distribution is estimated and methods for calculating expectations are studied. A connection is observed between the dimension and the complexity of the calculation of an expectation.

[1] P. McLane. Lower Bounds for Finite Intersymbol Interference Error Rates , 1974, IEEE Trans. Commun..

[2] L. Lorne Campbell,et al. Error probabilities on fading channels with intersymbol interference and noise , 1993, IEEE Trans. Inf. Theory.

[3] Norman C. Beaulieu,et al. The evaluation of error probabilities for intersymbol and cochannel interference , 1991, IEEE Trans. Commun..

[4] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .

[5] Carl W. Helstrom,et al. Calculating Error Probabilities for Intersymbol and Cochannel Interference , 1986, IEEE Trans. Commun..

[6] Thomas M. Cover,et al. Elements of Information Theory , 2005 .

[7] L. Lorne Campbell,et al. Infinite series of interference variables with Cantor-type distributions , 1988, IEEE Trans. Inf. Theory.

[8] Kenneth Falconer,et al. Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[9] Jean Kahane,et al. Sur la convolution d'une infinité de distributions de Bernoulli , 1958 .

[10] A. Wintner,et al. Distribution functions and the Riemann zeta function , 1935 .

[11] A. Garsia. Entropy and singularity of infinite convolutions. , 1963 .

[12] H. Eggleston. The fractional dimension of a set defined by decimal properties , 1949 .

[13] P. Billingsley,et al. Ergodic theory and information , 1966 .

[14] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1951 .