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

Quantization using permutation codes with a uniform source

Permutation coding is a block coding/quantization scheme where the codebook is comprised entirely of permutations of a single starting vector. Permutation codes for the uniform source are developed using a simple algorithm. The performance of these codes is com- pared against scalar codes and permutation codes developed by dierent methodologies. It is shown that the algorithm produces codes as good as other more complex methods. Theo- retical predictions of code design parameters and code performance is veried by numerical simulations

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

Study of sequential decoding

Decoding algorithms for data reduction and transmission through noisy space channels using sequential and hybrid computer