ČSN IEC 60050-171 - Mezinárodní elektrotechnický slovník – Část 171: Digitální technologie – Základní pojmy

171-07-27 mean transinformation content

$T\left(X,Y\right)={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^{m}p(x_i,y_j)\cdot T(x_i,y_j)}}$

where

X = {x₁, …, x_n} is the set of events x_i (i = 1, …, n), Y = {y₁, …, y_m} is the set of events y_j (j = 1, …, m) and p(x_i,y_j) the joint probability that both events occur

Note 1 to entry: The mean transinformation content is symmetric in X and Y. It is also equal to the difference between the entropy of one of the two sets of events and the conditional entropy of this set relative to the other: $T\left(X|Y\right)=H(X)-H(X|Y)=H(Y)-H(Y|X)=T(X|Y)$.

Note 2 to entry: The mean transinformation content is a quantitative measure of information transmitted through a channel, when X is a specific set of messages at the message source and Y is a specific set of messages at the message sink. It is equal to the difference between the entropy at the message source and the equivocation, or the difference between the entropy at the message sink and the irrelevance.