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Title: A study of index assignments
Author: Day, Jen-Der
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1999
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A nonredundant quantization system is extensively used in a noisy communication system. However, the removal of redundancy can introduce a great deal of sensitivity to the noise engendered by transmission and this can cause performance to degrade. Index assignment is a way of combating this degradation of performance. A good index assignment algorithm will minimize the channel distortion caused by channel errors, but since the error rate affects the channel distortion, the performance of an optimal index assignment will vary as the error rate varies. Therefore, it is important to develop an index assignment algorithm that minimizes the channel distortion and is robust against variation in error rate as well. The thesis will look at robust index assignment algorithms which minimize channel distortion for scalar and vector quantizations. An index assignment algorithm EIA for a scalar quantization model when the error rate is fixed is proposed. The idea behind the EIA is to use the Hadamard transformation and to rearrange the quantizer as close to the linear eigenspace as possible. Technically, the EIA depends on a regression calculation and sorting algorithm. Secondly, a modification of EIA, SEIA is presented which is independent of the initial index assignment. Thirdly, an algorithm VEIA which extends the EIA for scalar quantization to vector quantization is proposed. As well as existing criterion, a new criterion, the expected channel distortion (ECD) is defined on a beta-type prior density function for error rate which is appropriate for situations where the error rate varies over time. The above three algorithms are measured under this and the criterion is shown to perform well. To illustrate the performances of signal-to-noise ratio, efficiency and robustness, the EIA is compared with the well-known algorithm BSA by using real data - a voice digitization in North American Telephone Systems CCITT for scalar quantization. For vector quantization, VEIA is compared with the algorithm BSA by using first-order Gauss-Markov data. The signal-to-noise ratio performance between EIA and BSA or VEIA and BSA are shown to be indistinguishable. The calculations involved in EIA, SEIA and VEIA are very simple since only a sorting algorithm is required. EIA takes on 0.9 seconds for a 256-point real world scalar quantizer while BSA takes hours. VEIA requires only 8 seconds for a two-dimension vector quantizer of size 256 when BSA again takes hours. Also, EIA and VEIA are robust when the error rate changes. They give the same optimal index assignments for error rate varying from 0.00001 to 0.1, while the BSA algorithm leads to different assignments.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available