On concentric spherical codes and permutation codes with multiple initial codewords

Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure. In this paper, we provide an extension that preserves the computational simplicity but yields improved operational rate-distortion performance. 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.