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Rate-Distortion Functions for Nonstationary Gaussian Autoregressive Processes

9 years 1 months ago
Rate-Distortion Functions for Nonstationary Gaussian Autoregressive Processes
Source coding theorems and Shannon rate-distortion functions were studied for the discrete-time Wiener process by Berger and generalized to nonstationary Gaussian autoregressive processes by Gray and by Hashimoto and Arimoto. Hashimoto and Arimoto provided an example apparently contradicting the methods used in Gray, implied that Gray's rate-distortion evaluation was not correct in the nonstationary case, and derived a new formula that agreed with previous results for the stationary case and held in the nonstationary case. In this correspondence it is shown that the rate-distortion formulas of Gray and Hashimoto and Arimoto are in fact consistent and that the example of Hashimoto and Arimoto does not form a counterexample to the methods or results of the earlier paper. Their results do provide an alternative, but equivalent, formula for the rate-distortion function in the nonstationary case and they provide a concrete example that the classic Kolmogorov formula differs from the a...
Robert M. Gray, Takeshi Hashimoto
Added 25 Dec 2009
Updated 25 Dec 2009
Type Conference
Year 2008
Where DCC
Authors Robert M. Gray, Takeshi Hashimoto
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