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arXiv · 1809.05968

The Structure of the Realizations of the Causal Information Rate-Distortion Function for Markovian Sources: Realizations with Densities

Milan S. Derpich
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Abstract

The main purpose of this note is to show that in a realization $(x_{1}^{n}, y_{1}^{n})$ of the causal \textit{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 $\ell$ for which $y_{k} \leftrightarrow y_{1}^{k-1},x_{k-\ell+1}^{k} \leftrightarrow x_{1}^{k-\ell}$ holds is $\ell=κ$. 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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Milan S. Derpich. 2018-09-16. The Structure of the Realizations of the Causal Information Rate-Distortion Function for Markovian Sources: Realizations with Densities. https://arxiv.org/abs/1809.05968

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