论文标题
通信通道优化分区
Communication-Channel Optimized Partition
论文作者
论文摘要
给定具有分布p_x的原始离散源x，该分布被噪声损坏，以产生给定关节分布p（x，y）的噪声数据y。然后，使用量化器/分类器q：y-> z将数据y与概率分布p_z进行分类/量化为离散的分区z。接下来，Z通过给定的通道矩阵A在确定性通道上传输，该通道矩阵A会产生最终离散输出T。一个人希望设计最佳的量化器/分类器q^*，以使输入X和最终输出t之间的成本函数f（x; t）最小化，而分区z的概率z可以满足凹凸构造的g（p_z p _ fonefent g（p _ z）的概述。首先，提出了迭代线性时间复杂算法以找到局部最佳量化器。其次，我们表明，最佳分区应产生一个硬分区，与后验概率p（x | y）的概率空间中的超平面剪切相同。最终，该结果提供了多项式时间算法，以找到全球最佳量化器。
Given an original discrete source X with the distribution p_X that is corrupted by noise to produce the noisy data Y with the given joint distribution p(X, Y). A quantizer/classifier Q : Y -> Z is then used to classify/quantize the data Y to the discrete partitioned output Z with probability distribution p_Z. Next, Z is transmitted over a deterministic channel with a given channel matrix A that produces the final discrete output T. One wants to design the optimal quantizer/classifier Q^* such that the cost function F(X; T) between the input X and the final output T is minimized while the probability of the partitioned output Z satisfies a concave constraint G(p_Z) < C. Our results generalized some famous previous results. First, an iteration linear time complexity algorithm is proposed to find the local optimal quantizer. Second, we show that the optimal partition should produce a hard partition that is equivalent to the cuts by hyper-planes in the probability space of the posterior probability p(X|Y). This result finally provides a polynomial-time algorithm to find the globally optimal quantizer.
