33 research outputs found
Randomized Quantization and Source Coding with Constrained Output Distribution
This paper studies fixed-rate randomized vector quantization under the
constraint that the quantizer's output has a given fixed probability
distribution. A general representation of randomized quantizers that includes
the common models in the literature is introduced via appropriate mixtures of
joint probability measures on the product of the source and reproduction
alphabets. Using this representation and results from optimal transport theory,
the existence of an optimal (minimum distortion) randomized quantizer having a
given output distribution is shown under various conditions. For sources with
densities and the mean square distortion measure, it is shown that this optimum
can be attained by randomizing quantizers having convex codecells. For
stationary and memoryless source and output distributions a rate-distortion
theorem is proved, providing a single-letter expression for the optimum
distortion in the limit of large block-lengths.Comment: To appear in the IEEE Transactions on Information Theor
Common Information Approach for Static Team Problems with Polish Spaces and Existence of Optimal Policies
In this paper, we demonstrate the existence of team-optimal strategies for
static teams under observation-sharing information structures. Assuming that
agents can access shared observations, we begin by converting the team problem
into an equivalent centralized stochastic control problem through the
introduction of a topology on policies. We subsequently apply conventional
methods from stochastic control to prove the existence of team-optimal
strategies. This study expands upon the widely recognized common information
approach for team problems, originally designed for discrete scenarios, and
adapts it to a more abstract continuous framework. The primary difficulty in
this context is to establish the appropriate topology on policies.Comment: arXiv admin note: text overlap with arXiv:1711.0063