A connection between good rate-distortion codes and backward DMCs
Curt M. Schieler, Paul Cuff · 2013
Let Xnϵ Xnbe a sequence drawn from a discrete memoryless source, and let Ynϵ ynbe the corresponding reconstruction sequence that is output by a good rate-distortion code. This paper establishes a property of the joint distribution of (Xn, Yn). It is shown that for D > 0, the input-output statistics of a R(D)-achieving rate-distortion code converge (in normalized relative entropy) to the output-input statistics of a discrete memoryless channel (dmc). The dmc is “backward” in that it is a channel from the reconstruction space ynto source space Xn. It is also shown that the property does not necessarily hold when normalized relative entropy is replaced by variational distance.