Variable Fanout

Data compression attempts to reduce the amount of information needed to recreate a signal. A source coder is a data compression system which attempts to maximize the quality of the signal reproduction for a xed transmission rate or minimize the transmission rate for a xed reproduction quality. Source coders are designed by exploiting the statistics of their signal sources. A vector quantizer can be used as a source coder. In this thesis, a generalized pruning technique called trimming is introduced which improves upon the performance of pruned tree-structured vector quantization. The algorithm designs a large balanced nonbinary tree and trims it back to create useful lower-rate subtrees. Trimming di ers from pruning in that it does not necessarily remove all descendants of the node being trimmed. However, appropriate codebook replacement is performed during each trim so that all codevectors within the trimmed subtree represent the centroids of their encoding cells. With trimming replacing pruning, the generalized BFOS algorithm of Chou, Lookabaugh, and Gray still identi es those subtrees which lie on the lower convex hull of the initial tree's operational distortion-rate function. It is shown experimentally that this new convex hull is often lower than the one found using pruning. In this sense, the new algorithm outperforms pruned tree-structured vector quantization. Both algorithms are allowed to time share at rates where no subtrees are located. To design the initial balanced nonbinary tree, it is su cient to specify the number of children each tree node will have. However, a constraint is imposed so that all nodes located at the same depth within the initial tree have the same number of children. For a given maximum rate constraint, there are clearly many iii initial tree structures which could be used. Specifying the initial tree structure is an extra degree of freedom not found with binary pruned tree-structured vector quantization. The new algorithm identi es the nonbinary tree which is optimal with respect to the transmission statistics of a multirate channel. Experimental results are supplied which demonstrate this performance. iv ACKNOWLEDGEMENTS I thank my advisor, Professor Kenneth Zeger, for guiding my research during the past two years. His numerous helpful suggestions made a vast improvement in the quality of this work and my abilities as a practicing engineer. This work was supported in part by a National Science Foundation Graduate Research Fellowship. v TABLE OF CONTENTS Page