Generalizations of permutation source codes

Abstract

Permutation source codes are a class of structured vector quantizers with a computationally- simple encoding procedure. In this thesis, we provide two extensions that preserve the computational simplicity but yield improved operational rate-distortion performance. In the first approach, the new class of vector quantizers has a codebook comprising several permutation codes as subcodes. Methods for designing good code parameters are given. One method depends on optimizing the rate allocation in a shape-gain vector quantizer with gain-dependent wrapped spherical shape codebook. In the second approach, we introduce frame permutation quantization (FPQ), 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 and quadratic programming are derived. 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. Simulations for uniform and Gaussian sources show performance improvements over entropy-constrained scalar quantization for certain combinations of vector dimension and coding rate.