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Adding controlled noise from predetermined distributions is a way of designing differentially private mechanisms. This technique is useful for designing private mechanisms for real-valued functions on sensitive data. Some commonly used distributions for adding noise include Laplace and Gaussian distributions.
Gaussian because it has a normal distribution in the time domain with an average time domain value of zero (Gaussian process). Wideband noise comes from many natural noise sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson–Nyquist noise ), shot noise , black-body radiation from the earth ...
In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). [1] [2] In other words, the values that the noise can take are Gaussian-distributed.
The key insight of differential privacy is that as the query is made on the data of fewer and fewer people, more noise needs to be added to the query result to produce the same amount of privacy. Hence the name of the 2006 paper, "Calibrating noise to sensitivity in private data analysis." [citation needed]
Noise having a continuous distribution, such as a normal distribution, can of course be white. It is often incorrectly assumed that Gaussian noise (i.e., noise with a Gaussian amplitude distribution – see normal distribution) necessarily refers to white noise, yet neither property implies the other. Gaussianity refers to the probability ...
In the simple version above, the signal and noise are fully uncorrelated, in which case + is the total power of the received signal and noise together. A generalization of the above equation for the case where the additive noise is not white (or that the / is not constant with frequency over the bandwidth) is obtained by treating the channel as many narrow, independent Gaussian ...
First, white noise is a generalized stochastic process with independent values at each time. [12] Hence it plays the role of a generalized system of independent coordinates, in the sense that in various contexts it has been fruitful to express more general processes occurring e.g. in engineering or mathematical finance, in terms of white noise.
An application of the channel capacity concept to an additive white Gaussian noise (AWGN) channel with B Hz bandwidth and signal-to-noise ratio S/N is the Shannon–Hartley theorem: C = B log 2 ( 1 + S N ) {\displaystyle C=B\log _{2}\left(1+{\frac {S}{N}}\right)\ }