Optimal Dual Frames for Communication Coding With Probabilistic Erasures
Optimal Dual Frames for Communication Coding With Probabilistic Erasures
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DOI：
10.1109/tsp.2011.2162955
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发表时间：
2011-11
影响因子：
5.4
通讯作者：
Jinsong Leng;D. Han;Tingzhu Huang
中科院分区：
文献类型：
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作者：
Jinsong Leng;D. Han;Tingzhu Huang
假设在通信系统中为编码预先选择了一个帧。从帧的数学理论出发，研究了在传输过程中出现概率擦除时，使最大误差最小的信号重构（译码）的最佳双帧。我们建立了一个概率模型，在该模型下，当基于帧的编码涉及概率擦除时，我们定义了给定帧的概率最优（PO）双帧。得到了正则对偶框架是唯一PO对偶框架的充分必要条件。此外，我们还导出了正则对偶框架不最优或最优但不是唯一最优的一般充分条件。我们给出了两个仿真实例来比较PO双帧和一般最优（GO）双帧进行重构的效果。
Assume that a frame is preselected for encoding in a communication system. We investigate the optimal dual frames for signal reconstruction (decoding) which minimize the maximal error when the probabilistic erasures occur in the transmission process from the perspective of mathematical theory of frames. We set up a probability model under which we define the probability optimal (PO) dual frames for a given frame when the frame-based coding involves probabilistic erasures. We obtain a sufficient and necessary condition under which the canonical dual frame is the unique PO dual frame. Additionally, we derive some general sufficient conditions for which the canonical dual frame is either not optimal or it is optimal but not the unique optimal one. We present two simulation examples to compare the reconstruction effects when both the PO dual frames and the general optimal (GO) dual frames are used for reconstruction.