Chapter 9 - Scalar Quantization

Abstract

In this chapter, we begin our study of quantization, one of the simplest and most general ideas in lossy compression. We will look at scalar quantization and continue with vector quantization in the next chapter. First, the general quantization problem is stated, then various solutions are examined, starting with the simpler solutions, which require the most assumptions, and proceeding to more complex solutions that require fewer assumptions. We describe uniform quantization with fixed-length codewords, first assuming a uniform source, then a source with a known probability density function (pdf) that is not necessarily uniform, and finally a source with unknown or changing statistics. We then look at pdf-optimized nonuniform quantization, followed by companded quantization. Finally, we return to the more general statement of the quantizer design problem and study entropy-coded quantization.