Thresholding Quantizer Design for Mutual Information Maximization Under Output Constraint
Thuan Nguyen, Thinh Nguyen · 2020
We consider a channel with discrete input X, a continuous noise that corrupts the input X 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. The goal is to jointly design a thresholding quantizer that maximizes the mutual information between input and quantized output I(X; V ) while minimizing a pre-specified function of the quantized output F(pV). A general dynamic programming algorithm is proposed having the time complexity O(KNM2) where N, M and K are the sizes of input X, output U and quantized output V, respectively. Moreover, we show that if F(pV) Σi=1Kgi(p(vi)) where gi(.) is a convex function, p(vi) ∈ pV{pv1,..., pvK} is the probability mass function of output vi∈ V and the channel conditional density p(u|x) satisfies the dominated condition (often true in practice), then the existing SMAWK algorithm can be applied to reduce the time complexity of the dynamic programming algorithm from O(KNM2) to O(KNM). Both theoretical and numerical results are provided to verify our contributions.