MetadataShow full item record
First author draft
Citation (published version)Alankrita Bhatt, Bobak Nazer, Or Ordentlich, Yury Polyanskiy. 2018. "Information-Distilling Quantizers." 2017 IEEE International Symposium on Information Theory (ISIT), https://doi.org/10.1109/ISIT.2017.8006497
Let X and Y be dependent random variables. This paper considers the problem of designing a scalar quantizer for Y to maximize the mutual information between the quantizer's output and X, and develops fundamental properties and bounds for this form of quantization, which is connected to the log-loss distortion criterion. The main focus is the regime of low I(X;Y), where it is shown that, if X is binary, a constant fraction of the mutual information can always be preserved using O(log(1/I(X;Y))) quantization levels, and there exist distributions for which this many quantization levels are necessary. Furthermore, for larger finite alphabets 2<|X|<∞, it is established that an η-fraction of the mutual information can be preserved using roughly (log(|X|/I(X;Y)))^(η⋅(|X|−1)) quantization levels.