<p> Codes with a tree structure find wide use in data compression and error correction. It is generally impractical to view and weigh all the branches in a code tree, so a search algorithm is employed which considers some but not others in a predetermined fashion. Traditionally, the efficiency of code tree search algorithms has been measured by the number of tree branches visited for a given level of performance. This measure does not indicate the true consumption of resources. Cost functions are defined based on the number of code tree paths retained, S, the length of the paths, L, and the number of code tree branches searched per branch released as output, E[C]. Using these cost functions, most of the existing algorithms as well as some new algorithms proposed here are compared.</p> <p> These new algorithms include three metric-first algorithms. The first one, the merge algorithm, uses, in addition to the main list used by the stack algorithm, an auxiliary list to store paths. The merge algorithm reduces the dependence on S for the product resource cost from O(S^2) for the stack algorithm to O(S^4/3 ) for the merge algorithm. A generalization of this algorithm reduces the product cost to O(S log S). The second algorithm uses a class of height-balanced trees, known as AVL trees, to store code tree paths, resulting in an alternate method to the merge algorithm achieving O(S log S) cost.</p> <p> The third algorithm, using the concepts of dynamic hashing and trie searching, provides important modifications to the Jelinek bucket algorithm by incorporating dynamic splitting and merging of buckets. This strategy provides a
balanced data structure and reduces the product cost still further compared to the first two algorithms.</p> <p> We next turn to analysis of the number of nodes visited during a search. Using the theory of multitype branching processes in random environments an equation for node computation is derived for asymmetric source coding by the single stack algorithm. This equation is shown to be the stochastic analog of an equation for symmetric sources. Simulation results, obtained by encoding the Hamming source by the single stack algorithm, are used to optimize the performance of the algorithm with respect to the bias
factor, stack length, and limit on computation. A modification to the algorithm that raises the barrier during forward motion provides a better distortion performance.</p> <p> The metric-first stack algorithm is used to encode a voiced speech sound. From experimental evidence, it is shown how to optimize the algorithm's SNR performance with respect to the algorithm's storage, execution time, and node computation. For each of these, the optimal parameterizing
of the algorithm differs markedly. Similarities are pointed out between the results for speech and earlier theoretical results for the binary i.i.d. source with Hamming distortion measure. It is shown that metric-first algorithms may perform better with "real life" sources like speech than they do with artificial sources, and in view of this the algorithms proposed here take on added significance.</p> / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19692 |
| Date | 09 1900 |
| Creators | Mohan, Seshadri |
| Contributors | Anderson, J. B., Electrical Engineering |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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