187 research outputs found
Frame Permutation Quantization
Frame permutation quantization (FPQ) is a new vector quantization technique
using finite frames. In FPQ, a vector is encoded using a permutation source
code to quantize its frame expansion. This means that the encoding is a partial
ordering of the frame expansion coefficients. Compared to ordinary permutation
source coding, FPQ produces a greater number of possible quantization rates and
a higher maximum rate. Various representations for the partitions induced by
FPQ are presented, and reconstruction algorithms based on linear programming,
quadratic programming, and recursive orthogonal projection are derived.
Implementations of the linear and quadratic programming algorithms for uniform
and Gaussian sources show performance improvements over entropy-constrained
scalar quantization for certain combinations of vector dimension and coding
rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared
error (MSE) decays as 1/M^4 for an M-element frame, which is consistent with
previous results on optimal decay of MSE. Reconstruction using the canonical
dual frame is also studied, and several results relate properties of the
analysis frame to whether linear reconstruction techniques provide consistent
reconstructions.Comment: 29 pages, 5 figures; detailed added to proof of Theorem 4.3 and a few
minor correction
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
Concentric Permutation Source Codes
Permutation codes are a class of structured vector quantizers with a
computationally-simple encoding procedure based on sorting the scalar
components. Using a codebook comprising several permutation codes as subcodes
preserves the simplicity of encoding while increasing the number of
rate-distortion operating points, improving the convex hull of operating
points, and increasing design complexity. We show that when the subcodes are
designed with the same composition, optimization of the codebook reduces to a
lower-dimensional vector quantizer design within a single cone. Heuristics for
reducing design complexity are presented, including an optimization of the rate
allocation in a shape-gain vector quantizer with gain-dependent wrapped
spherical shape codebook
Information-Distilling Quantizers
Let and be dependent random variables. This paper considers the
problem of designing a scalar quantizer for to maximize the mutual
information between the quantizer's output and , and develops fundamental
properties and bounds for this form of quantization, which is connected to the
log-loss distortion criterion. The main focus is the regime of low ,
where it is shown that, if is binary, a constant fraction of the mutual
information can always be preserved using
quantization levels, and there exist distributions for which this many
quantization levels are necessary. Furthermore, for larger finite alphabets , it is established that an -fraction of the
mutual information can be preserved using roughly quantization levels
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