Multistage storage- and entropy-constrained tree-structured vector quantization

This paper proposes a new algorithm for the design of a tree-structured vector quantizer that operates under storage and entropy constraints; hence, it is called the storage- and entropy-constrained tree-structured vector quantizer (SECTSVQ). The algorithm uses the tree-growing approach and designs the tree one stage/layer at a time. The constraints on the rate and storage size, i.e., the number of nodes or codewords, at each stage are specified prior to the design procedure. While growing the tree, at each stage the algorithm optimally allocates the rate and the number of nodes available for the current stage to the nodes of the previous stage using the dynamic programming technique. The nodes of the current stage are then determined based on the allocations. In addition to being useful as a tree-structured VQ, SECTSVQ is particularly suited for application in progressive transmission. Moreover, the optimal allocation technique used in the design can be effectively applied to other optimal resource allocation problems. The SECTSVQ algorithm is implemented for various sources and is shown to compare favorably with other VQs.