25,184 research outputs found
Entropy of Highly Correlated Quantized Data
This paper considers the entropy of highly correlated quantized samples. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary continuous-time random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of an infinite-level uniform threshold scalar quantizer and a stationary Gaussian random process. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived. At high sampling rates, these results indicate a sharp contrast between the large encoding rate (in bits/sec) required by a lossy source code consisting of a fixed scalar quantizer and an ideal, sampling-rate-adapted lossless code, and the bounded encoding rate required by an ideal lossy source code operating at the same distortion
Low-Resolution Scalar Quantization for Gaussian Sources and Absolute Error
This correspondence considers low-resolution scalar quantization for a memoryless Gaussian source with respect to absolute error distortion. It shows that slope of the operational rate-distortion function of scalar quantization is infinite at the point Dmax where the rate becomes zero. Thus, unlike the situation for squared error distortion, or for Laplacian and exponential sources with squared or absolute error distortion, for a Gaussian source and absolute error, scalar quantization at low rates is far from the Shannon rate-distortion function, i.e., far from the performance of the best lossy coding technique
Robust Hyperproperty Preservation for Secure Compilation (Extended Abstract)
We map the space of soundness criteria for secure compilation based on the
preservation of hyperproperties in arbitrary adversarial contexts, which we
call robust hyperproperty preservation. For this, we study the preservation of
several classes of hyperproperties and for each class we propose an equivalent
"property-free" characterization of secure compilation that is generally better
tailored for proofs. Even the strongest of our soundness criteria, the robust
preservation of all hyperproperties, seems achievable for simple
transformations and provable using context back-translation techniques
previously developed for showing fully abstract compilation. While proving the
robust preservation of hyperproperties that are not safety requires such
powerful context back-translation techniques, for preserving safety
hyperproperties robustly, translating each finite trace prefix back to a source
context seems to suffice.Comment: PriSC'18 final versio
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