Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 60, Issue 8, Pages 4544-4552Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2327016
Keywords
Discrete memoryless channel; channel quantization; mutual information maximization; classification and regression
Funding
- Ministry of Education, Science, Sports and Culture [23560439, 22760270]
- Japan Science and Technology Agency, Special Coordination Funds for Promoting Science and Technology
- Grants-in-Aid for Scientific Research [23560439, 22760270, 25420357] Funding Source: KAKEN
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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 Nadas for mappings, which minimize average impurity for classification and regression trees.
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