The Structure of the Realizations of the Causal Information Rate-Distortion Function for Markovian Sources: Realizations with Densities
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The main purpose of this note is to show that in a realization (x_1^n, y_1^n) of the causal information rate-distortion function (IRDF) for a κ-th order Markovian source x_1^n, under a single letter sum distortion constraint, the smallest integer ℓ for which y_k y_1^k-1,x_k-ℓ+1^k x_1^k-ℓ holds is ℓ=κ. This result is derived under the assumption that the sequences (x_1^n,y_1^n) have a joint probability density function.
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