Spectrally two-uniform frames for erasures
Spectrally two-uniform frames for erasures
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DOI：
10.7153/oam-09-23
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发表时间：
2015
影响因子：
0.5
通讯作者：
Saliha Pehlivan;D. Han;R. Mohapatra
中科院分区：
文献类型：
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作者：
Saliha Pehlivan;D. Han;R. Mohapatra
我们继续研究当谱半径用作误差算子的测量时表征擦除最佳帧的问题。一次擦除的光谱最佳(N,n)帧是可以实现最小光谱误差n/N的帧。此类帧在[28]中在相关帧的连通性和冗余分布方面得到了完整的表征。我们表明，两次擦除的最佳光谱误差始终大于或等于 n N + ( Nn−n2 N2(N−1) ) 1/2 。我们对所有框架进行表征，以便可以实现上述下限。当N=n+1或n+2时，也得到不同的表征。我们表明，在这些特殊情况下，谱 2 擦除最优帧与帧的 n 独立属性相关。数学科目分类（2010）：小学42C15、46C05、47B10。
We continue to work on the problem of characterizing erasure-optimal frames when spectral radius is used as a measurement of the error operator. Spectrally optimal (N,n) -frames for one erasures are the ones that the minimal spectral error n/N can be achieved. This class of frames was completely characterized in [28] in terms of the connectivity property and the redundancy distributions of the involved frames. We show that the best spectral error for the two erasures is always greater than or equal to n N + ( Nn−n2 N2(N−1) ) 1/2 . We characterize all the frames such that the above lower bound can be achieved. Different characterizations are also obtained for the case that when N = n + 1 or n + 2 . We show that in these special cases, spectrally 2-erasure optimal frames are related to the n -independence property of frames. Mathematics subject classification (2010): Primary 42C15, 46C05, 47B10.