Search

Necessary conditions for the optimality of variable-rate residual vector quantizers are derived, and an iterative descent algorithm based on a Lagrangian formulation is introduced for designing residual vector quantizers having minimum average distortion subject to an entropy constraint. Simulation results for entropy-constrained residual vector quantizers are presented for memoryless Gaussian, Laplacian, and uniform sources. A Gauss-Markov source is also considered. The rate-distortion performance is shown to be competitive with that of entropy-constrained vector quantization and entropy-constrained trellis-coded quantization. Index Terms - Vector quantization, residual vector quantization, entropy, source coding, and rate-distortion function.

The use of direct sum codebooks to minimize the memory requirements of vector quantizers is investigated. Assuming arbitrary fixed partitions, necessary conditions for minimum distortion codebooks are derived: first for scalar codebooks, assuming mean-squared error distortion, and then for vector codebooks and a broader class of distortion measures. An iterative procedure is described for designing locally optimal direct sum codebooks. Both optimal and computationally efficient suboptimal encoding schemes are considered. It is shown that although an optimal encoding can be implemented by a sequential encoder, the complexity of implementing optimal stagewise partitions generally exceeds the complexity of an exhaustive search of the direct sum codebook. It is also shown that sequential nearest-neighbor encoders, which encode each stagewise residual with the nearest-neighbor code vector from the associated stagewise codebook, can be extremely inefficient. This is particularly true for direct sum quantizers with high output rates or with many stages. The M-search method is explored as one method of improving the effectiveness of suboptimal sequential encoders. Representative results of simulated direct sum quantizers are presented for Laplacian, Gaussian and Gauss-Markov sources.

Presents a signal set construction technique that provides an efficient means for realizing multidimensional trellis-coded modulation (TCM). Reviews of definition and mathematical formulation of a sigma-tree geometric structures; Overview of sigma-tree TCM codes; Decoder structure.