非对称高斯多重描述与非对称多电平分集编码

S. Mohajer, C. Tian, S. Diggavi
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引用次数: 8

摘要

研究了均方误差失真约束下高斯源的非对称多重描述(MD)编码,重点研究了三种描述问题。导出了速率区域的内外边界,这两个边界都可以表示为十个具有匹配法线方向的半空间的交点。此外,内界和外界之间的间隙很小。内界依赖于我们早期工作中处理的无损非对称多层分集(MLD)编码问题的速率区域表征,这是Roche等人先前考虑的对称MLD编码问题的自然推广。与对称MLD编码不同,在非对称情况下,叠加编码是不够的,需要有策略地使用类似于网络编码的思想。根据这一发现,并受到对称MD和对称MLD编码之间联系的激励,在这项工作中,我们将非对称MD视为非对称MLD编码的有损版本,这需要超越简单叠加的编码。还导出了外界,它具有特别适合与内界比较的几何结构。结合内外边界,给出了非对称高斯三描述问题的速率区域的近似表征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymmetric Gaussian multiple descriptions and asymmetric multilevel diversity coding
We consider asymmetric multiple description (MD) source coding for Gaussian source under mean squared error distortion constraints, and focus on the three description problem. Inner and outer bounds for the rate region are derived, both of which can be represented as the intersection of ten half spaces with matching normal directions. Moreover, the gap between the inner and outer bounds is shown to be small. The inner bound relies on the rate region characterization of a lossless asymmetric multilevel diversity (MLD) coding problem treated in our earlier work, which is a natural generalization of the symmetric MLD coding problem previously considered by Roche et al. Different from symmetric MLD coding, superposition coding is not sufficient in the asymmetric case, and ideas akin to network coding need to be used strategically. Equipped with this finding, and motivated by the connection between symmetric MD and symmetric MLD coding, in this work we consider asymmetric MD as a lossy version of the asymmetric MLD coding, which requires coding beyond simple superposition. An outer bound is also derived, which bears a geometric structure particularly suitable for comparison with the inner bound. Combining the inner and outer bounds provides an approximate characterization of the rate region for the asymmetric Gaussian three description problem.
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