The entropy of a code with probabilities

The entropy of a code with probabilities is defined and as a consequence the concept of conservation of entropy in lossless source coding emerges in a natural manner. For any given probability distribution (p/sub 1/,p/sub 2/,...,p/sub T/) all the distinct decompositions of the associated entropy function h(p/sub 1/,p/sub 2/,...,p/sub T/), as a function of entropies of lower order, are obtained from the terminal uncertainty of the distinct rooted trees with leaf probabilities (p/sub 1/,p/sub 2/,...,p/sub T/).