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The Rate-Distortion-Perception Trade-off: The Role of Private Randomness
The per-symbol near-perfect realism constraint requires that the TVD between the distribution of output symbol $Y_t$ and the source distribution be arbitrarily small, uniformly in the index $t.$ We characterize the corresponding asymptotic rate-distortion trade-off and show that encoder private randomness is not useful if the compression rate is lower than the entropy of the source, however limited the resources in terms of common randomness and decoder private randomness may be.
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