Directed information
Directed information is an information theory measure that quantifies the information flow from the random string X n = ( X 1 , X 2 , … , X n ) {\displaystyle X^{n}=(X_{1},X_{2},\dots ,X_{n})} to the random string Y n = ( Y 1 , Y 2 , … , Y n ) {\displaystyle Y^{n}=(Y_{1},Y_{2},\dots ,Y_{n})} . The term directed information was coined by James Massey and is defined as I ( X n → Y n ) ≜ ∑ i = 1 n I ( X i ; Y i | Y i − 1 ) {\displaystyle I(X^{n}\to Y^{n})\triangleq \sum _{i=1}^{n}I(X^{i};Y_{i}|Y^{i-1})} where I ( X i ; Y i | Y i − 1 ) {\displaystyle I(X^{i};Y_{i}|Y^{i-1})} is the conditional mutual information I ( X 1 , X 2 , .