On the Statistical Physics of Directed Polymers in a Random Medium and Their Relation to Tree Codes
Using well-known results from statistical physics, concerning the almost-sure behavior of the free energy of directed polymers in a random medium, we prove that random tree codes achieve the distortion-rate function, not only on the average, but moreover, almost surely under a certain symmetry condition.
directed polymer tree coding free energy cayley tree delay partition function rate-distortion theory