Quantization and Coding

Abstract

After sampling, multimedia signal 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 often represented by continuous (or large sets of fine-granular discrete) amplitude values. To obtain a more compact digital representation, quantization is necessary. Quantization typically effects a distortion, which depends on the chosen quantizer step size and the number of quantization levels. On the other hand, the number of levels has direct influence on the rate that is necessary for representation. The relationship between rate and distortion is an important topic of information theory, by which the rate-distortion function and the source coding theorem were developed. The rate-distortion function defines the minimum rate to be provided for representation when a maximum distortion shall not be superseded, and depends on the statistic properties of a source. An analytic derivation is however only possible for stationary signal models. Statistical dependencies within source processes can implicitly be integrated into the rate-distortion dependency formulations. Following the statements of the source coding theorem, the minimum rate expressed by the rate-distortion function can be approached, if a large number of source symbols are encoded jointly, which can be implemented by block codes or sliding- block codes. Concrete methods to approach the rate-distortion bound for minimum-rate lossless representation of continuous and discrete signals are entropy coding, vector quantization, tree and trellis coding.