论文标题
关于二进制量化器的唯一性，以最大程度地提高互信息
On the Uniqueness of Binary Quantizers for Maximizing Mutual Information
论文作者
论文摘要
我们考虑了一个带有二进制输入X的通道被连续值噪声损坏，该噪声导致连续值输出y。最佳二进制量化器用于将连续值的输出y量化为最终的二进制输出z，以最大程度地提高共同信息i（x; z; z; z）。我们表明，当通道条件密度r（y）= p（y = y | x = 0）/ p（y = y | x = 1）的比率严格增加/减小函数时，具有单个阈值的量化器可以最大程度地提高共同信息。此外，我们表明，最佳量化器（可能具有多个阈值）是具有阈值向量的一个，其元素是所有常数r*> 0的r（y）= r*的解决方案。有趣的是，最佳常数r*是唯一的。这种唯一性属性允许快速算法实现，例如一分配算法来找到最佳量化器。我们的结果还使用替代基本证明证实了一些先前的结果。我们显示了一些将结果应用于具有加性高斯噪音的频道的数值示例。
We consider a channel with a binary input X being corrupted by a continuous-valued noise that results in a continuous-valued output Y. An optimal binary quantizer is used to quantize the continuous-valued output Y to the final binary output Z to maximize the mutual information I(X; Z). We show that when the ratio of the channel conditional density r(y) = P(Y=y|X=0)/ P(Y =y|X=1) is a strictly increasing/decreasing function of y, then a quantizer having a single threshold can maximize mutual information. Furthermore, we show that an optimal quantizer (possibly with multiple thresholds) is the one with the thresholding vector whose elements are all the solutions of r(y) = r* for some constant r* > 0. Interestingly, the optimal constant r* is unique. This uniqueness property allows for fast algorithmic implementation such as a bisection algorithm to find the optimal quantizer. Our results also confirm some previous results using alternative elementary proofs. We show some numerical examples of applying our results to channels with additive Gaussian noises.
