Multimedia data can be considered as data observed at the output of a source with memory. Sometimes we say that speech and images have considerable redundancy, meaning the statistical correlation or dependence between the samples of such sources which is referred to as memory in information theory literature. Scalar quantization does not exploit this redundancy or memory. As was shown in Chapter 3, scalar quantization for sources with memory provides a rate-distortion function which is rather far from the achievable rate-distortion function H(D) for a given source. Vector quantization could attain better rate-distortion performance but usually at the cost of significantly increasing computational complexity. Another approach leading to a better rate-distortion function and preserving rather low computational complexity combines linear processing with scalar quantization. First, we remove redundancy from the data and then apply scalar quantization to the output of the memoryless source. Outputs of the obtained memoryless source can be vector quantized with lower average distortions but with higher computational complexity. The two most important approaches of this variety are predictive coding and transform coding (Jayant and Noll 1984). The first approach is mainly used for speech compression and the second approach is applied to image, audio, and video coding. In this chapter, we will consider predictive coding systems which use time-domain operations in order to remove redundancy and thereby to reduce the bit-rate for given quantization error levels.