Analog coding of a source with erasures
Analog coding of a source with erasures
复制标题
带擦除的源的模拟编码
DOI：
10.1109/isit.2016.7541664
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
R. Zamir
中科院分区：
文献类型：
--
作者：
Marina Haikin;R. Zamir
模拟编码分离了防止擦除和噪声的任务。对于擦除校正，它通过带限离散傅立叶变换(DFT)内插，或者更一般地，通过基于帧的过度完整扩展来创建“模拟冗余”。我们研究了用于在编码器处设置具有“擦除”边信息(SI)的源的双重设置的模拟编码范例。高于速率失真函数(RDF)的模拟编码的过剩速率与帧的子矩阵的逆的能量相关联，其中每个子矩阵对应于可能的擦除模式。我们给出了一个部分的理论和数值证明，证明了各种结构框架，特别是具有差集谱的DFT框架和具有公共Manova极限谱的更一般的等角紧框架(ETF)，可以最小化所有可能框架的超额速率。然而，即使在尺寸达到无穷大的极限情况下，它们也不能达到RDF。
Analog coding decouples the tasks of protecting against erasures and noise. For erasure correction, it creates an “analog redundancy” by means of band-limited discrete Fourier transform (DFT) interpolation, or more generally, by an over-complete expansion based on a frame. We examine the analog coding paradigm for the dual setup of a source with “erasure” side-information (SI) at the encoder. The excess rate of analog coding above the rate-distortion function (RDF) is associated with the energy of the inverse of submatrices of the frame, where each submatrix corresponds to a possible erasure pattern. We give a partial theoretical as well as numerical evidence that a variety of structured frames, in particular DFT frames with difference-set spectrum and more general equiangular tight frames (ETFs), with a common MANOVA limiting spectrum, minimize the excess rate over all possible frames. However, they do not achieve the RDF even in the limit as the dimension goes to infinity.