9 - Transform coding systems

Summary

Introduction

In previous chapters, we described mathematical transformations that produce nearly uncorrelated elements and pack most of the source energy into a small number of these elements. Distributing the code bits properly among these transform elements, which differ statistically, leads to coding gains. Several methods for optimal rate distribution were explained in Chapter 8. These methods relied on knowledge of the distortion versus rate characteristics of the quantizers of the transform elements. Using a common shape model for this characteristic and the squared error distortion criterion meant that only the variance distribution of the transform elements needed to be known. This variance distribution determines the number of bits to represent each transform element at the encoder, enables parsing of the codestream at the decoder and association of decoded quantizer levels to reconstruction values. The decoder receives the variance distribution as overhead information. Many different methods have arisen to minimize this overhead information and to encode the elements with their designated number of bits. In this chapter, we shall describe some of these methods.

Application of source transformations

A transform coding method is characterized by a mathematical transformation or transform of the samples from the source prior to encoding. We described the most common of these transforms in Chapter 7. The stream of source samples is first divided into subblocks that are normally transformed and encoded independently.