Information flow (information theory)

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Information flow (information theory)

Information flow in an information theoretical context is the transfer of information from a variable "h" to a variable "l" in a given process. The measure of information flow, "p", is defined as the uncertainty before the process started minus the uncertainty after the process has terminated. This can be quantified as

:$H\left(h|l\right) - H\left(h|l\text{'}\right) stackrel\left\{mathrm\left\{def\left\{=\right\} \left(H\left(h,l\right) - H\left(l\right)\right) - \left(H\left(h,l\text{'}\right) - H\left(l\text{'}\right)\right),!$

where $H\left(h|l\right)$ is the conditional entropy (equivocation) of variable "h" (before the process started) given the variable "l" (before the process started), and $H\left(h|l\text{'}\right)$ is the conditional entropy (equivocation) of variable "h" (before the process started) given the variable "l"' (the value of variable "l" after the process finished).

$H\left(X,Y\right)$ is the joint entropy, and can be calculated as follows:

:$H\left(X,Y\right) = -sum_\left\{x,y\right\} p_\left\{x,y\right\} log\left(p_\left\{x,y\right\}\right) !$

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