标题： 通信信道优化划分 显示英文标题

标题： Communication-Channel Optimized Partition

摘要： 给定一个原始离散信源 X，其分布为 p_X，通过噪声干扰产生带有给定联合分布 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 分类/量化为具有概率分布 p_Z 的离散分区输出 Z。 接下来，Z 通过具有给定信道矩阵 A 的确定性信道传输，产生最终的离散输出 T。 人们希望设计最优的量化器/分类器 Q^*，使得输入 X 和最终输出 T 之间的代价函数 F(X; T) 最小化，同时分区输出 Z 的概率满足一个凹约束 G(p_Z) < C。 我们的结果推广了一些著名的先前结果。 首先，提出了一种迭代线性时间复杂度算法来找到局部最优的量化器。 其次，我们证明了最优的分区应该产生一个硬分区，这等价于后验概率 p(X|Y) 概率空间中的超平面切割。 这一结果最终提供了一个多项式时间算法来找到全局最优的量化器。 显示英文摘要

摘要： 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.