Vector quantizer design using genetic algorithms

Abstract

The design of vector quantizers (VQs) that yield minimal distortion is one of the most challenging problems in source coding. The problem of VQ design is to find a codebook that gives the least overall distortion (or equivalently, the largest signal-to-noise ratio (SNR)) for a given set of input vectors. This problem is known to be difficult as there are no known closed-form solutions. The generalized Lloyd algorithm (GLA) uses a finite set of training sequences as the data source and employs an iterative refinement. Given an initial codebook, the algorithm computes the nearest focally optimum codebook only. Genetic algorithms (GAs) are emerging as widely accepted optimization and search methods. These search methods are rooted in the mechanisms of evolution and natural genetics. They have a high probability of locating the globally optimal solution in a multimodal search space. A genetic algorithmic (GA) approach to vector quantizer design that combines the GLA is presented. We refer to this hybrid as the genetic generalized Lloyd algorithm (GGLA). It works briefly as follows. Initially, a finite number of codebooks, called chromosomes, are selected. In contrast to the GLA which refines only one codebook at a time, those codebooks undergo iterative cycles of reproduction in parallel. During an iteration, each codebook is updated by GLA or GA operations (i.e., mutation, crossover, and chromosome replacement). Three versions of the GGLAs are investigated depending on how the GLA or GA is selected.