Consider a channel having the discrete input X that is corrupted by a continuous noise to produce the continuous-valued output U. A thresholding quantizer is then used to quantize the continuous-valued output U to the final discrete output V. One wants to design a thresholding quantizer that maximizes the mutual information between the input and the final quantized output I(X;V). In this paper, the structure of optimal thresholding quantizer is established that finally results in two efficient algorithms having the time complexities $O(NM+K\log^{2}(NM))$ for finding the local optimal quantizer and $O(KM\log(NM))$ for finding the global optimal quantizer where N, M, K are the size of input X, received output U and quantized output V, respectively. Both theoretical and numerical results are provided to verify our contributions.
On Thresholding Quantizer Design for Mutual Information Maximization: Optimal Structures and Algorithms
2020-05-01
136789 byte
Conference paper
Electronic Resource
English
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