Quantization and Coding

Abstract

By sampling, multimedia signals are discrete in space and/or time. Transformed equivalents of these signals, e.g. frequency coefficients or prediction error signals, and feature values or parameters related to these signals are formally represented by continuous (or large number of discrete) amplitude values. For compact coding, further quantization has to be employed, which causes distortion. The quantization step size and the range of amplitudes determine the necessary number of levels and the rate necessary for binary representation. The relationship between rate and distortion is expressed by the rate distortion function, for which a lower bound is expressed by the source coding theorem. An analytic derivation of the R-D bound is straightforward for stationary processes, which is useful in understanding basic limitations of source coding for real world signals. Statistical dependencies within sources also need to be considered in the rate-distortion dependency. Basic methods suitable to approach the rate-distortion bound for minimum-rate representation of continuous and discrete sources are also discussed in this chapter, including various approaches of entropy coding, vector quantization, tree and trellis coding.