论文标题
在任意量化输出约束下，二进制离散输入连续输出通道的最佳量化结构
Optimal quantizer structure for binary discrete input continuous output channels under an arbitrary quantized-output constraint
论文作者
论文摘要
给定具有二进制输入x =（x_1，x_2）的通道，其概率分布p_x =（p_ {x_1}，p_ {x_2}），该频率被连续的噪声损坏，以产生连续的输出y \ in y =R。连续输出y回到最终离散输出z =（z_1，z_2，...，z_n），具有n \ leq 2，使得输入和量化输出i（x; z）之间的相互信息是最大化的，而量化量化output p_z =（p_ {z_1}，p__1}，p__2}，z___2}，z_______，p_______，p__，p__，p__，p__，p_______，考虑一个新的变量r_y = p_ {x_1} ϕ_1（y）/（p_ {x_1} ϕ_1（y）+p_1（y）+p_ {x_2} ϕ_2（y）），我们表明，最佳量化器具有新的可变量r_y的convex单元的结构。根据最佳量化器的凸单元性能，提出了一种快速算法以在多项式时间复杂性中找到全局最佳量化器。
Given a channel having binary input X = (x_1, x_2) having the probability distribution p_X = (p_{x_1}, p_{x_2}) that is corrupted by a continuous noise to produce a continuous output y \in Y = R. For a given conditional distribution p(y|x_1) = ϕ_1(y) and p(y|x_2) = ϕ_2(y), one wants to quantize the continuous output y back to the final discrete output Z = (z_1, z_2, ..., z_N) with N \leq 2 such that the mutual information between input and quantized-output I(X; Z) is maximized while the probability of the quantized-output p_Z = (p_{z_1}, p_{z_2}, ..., p_{z_N}) has to satisfy a certain constraint. Consider a new variable r_y=p_{x_1}ϕ_1(y)/ (p_{x_1}ϕ_1(y)+p_{x_2}ϕ_2(y)), we show that the optimal quantizer has a structure of convex cells in the new variable r_y. Based on the convex cells property of the optimal quantizers, a fast algorithm is proposed to find the global optimal quantizer in a polynomial time complexity.
