Quantization of Binary-Input Discrete Memoryless Channels

The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm, which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input and quantizer output is given. This result holds for arbit...

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Bibliographic Details
Published in:IEEE transactions on information theory 2014-08, Vol.60 (8), p.4544-4552
Main Authors: Kurkoski, Brian M., Yagi, Hideki
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Channels
Classification
Complexity theory
Counters
Exact sciences and technology
Impurities
Information theory
Information, signal and communications theory
Mapping
Memoryless systems
Mutual information
Optimization
Quantization
Quantization (signal)
Regression analysis
Sampling, quantization
Signal and communications theory
Telecommunications and information theory
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Summary:The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm, which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input and quantizer output is given. This result holds for arbitrary channels, in contrast to previous results for restricted channels or a restricted number of quantizer outputs. In the worst case, the algorithm complexity is cubic M 3 in the number of channel outputs M. Optimality is proved using the theorem of Burshtein, Della Pietra, Kanevsky, and Nádas for mappings, which minimize average impurity for classification and regression trees.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2327016