Low-rate vector quantizers are designed and simulated for highly correlated Gauss-Markov sources and the resulting performance is compared with Arnstein's optimized predictive quantizer and with Huang and Schultheiss' optimized transform coder. Two implementations of vector quantizers are considered: full search vector quantizers-which are optimal but require large codebook searches-and tree searched vector quantizers-which are suboptimal but require far less searching. The various systems are compared on the basis of performance, complexity, and generality of design techniques.

New algorithms for the design of trellis encoding data compression systems are described. The mare algorithm uses a training sequence of actual data from a source to improve an initial trellis decoder. An additional algorithm extends the constraint length of a given decoder. Combined, these algorithms allow the automatic design of a trellis encoding system for a particular source. The algorithms' effectiveness for random sources is demonstrated through performance comparisons with other source coding systems and with theoretical bounds. The algorithms are applied to the practical problem of the design of trellis and hybrid codes for medium-to-lowrate speech compression.

An efficient and intuitive algorithm is presented for the design of vector quantizers based either on a known probabilistic model or on a long training sequence of data. The basic properties of the algorithm are discussed and demonstrated by examples. Quite general distortion measures and long blocklengths are allowed, as exemplified by the design of parameter vector quantizers of ten-dimensional vectors arising in Linear Predictive Coded (LPC) speech compression with a complicated distortion measure arising in LPC analysis that does not depend only on the error vector.

The problem of designing a good decoder for a timeinvariant tree-coding data compression system is equivalent to that of finding a good low rate "fake process" for the original source, where the fake is produced by a time-invariant nonlinear filtering of an independent, identically distributed sequence of uniformly distributed discrete random variables and "goodness" is measured by the\bar{\rho}-distance between the fake and the original source. Several simple ad hoc techniques for obtaining such fake processes are introduced and shown by simulation to provide an improvement of typically 1-2 dB over optimum quantization, delta modulation, and predictive quantization for one-bit per symbol compression of Gaussian memoryless, autoregressive, and moving average sources. In addition, the fake process viewpoint provides a new intuitive explanation of why delta modulation and predictive quantization work as well as they do on Gaussian autoregressive sources.