Information-Distilling Quantizers

Let X and Y be dependent random variables. This paper considers the problem of designing a scalar quantizer for to maximize mutual information between quantizer's output X, develops fundamental properties bounds this form quantization, which is connected log-loss distortion criterion. The main focus regime low I(X;Y), where it shown that, if binary, constant fraction can always preserved using O (log(1/I(X;Y))) quantization levels, there exist distributions many levels are necessary. Furthermore, larger finite alphabets 2 <; | xmlns:xlink="http://www.w3.org/1999/xlink">X ?, established that an ?-fraction roughly (log(| /I(X;Y))) ?·(|X| - 1) levels.