# Concentric Permutation Source Codes

## TL;DR

This paper introduces concentric permutation source codes, a structured vector quantization method that enhances rate-distortion performance by combining multiple permutation codes with optimized codebook design and reduced complexity heuristics.

## Contribution

It proposes a novel concentric permutation source code framework, simplifying codebook optimization and improving rate-distortion trade-offs compared to traditional permutation codes.

## Key findings

- Enhanced rate-distortion performance with multiple subcodes
- Reduced codebook design complexity via lower-dimensional optimization
- Effective heuristics for shape-gain vector quantizer optimization

## Abstract

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.