论文标题
可实现的精制渐近学用于使用高斯密码手册连续完善
Achievable Refined Asymptotics for Successive Refinement Using Gaussian Codebooks
论文作者
论文摘要
我们研究了不匹配的连续精炼问题，其中人们使用高斯密码手册来压缩任意内存的源，连续的最小欧几里得距离在二次失真度量下编码。具体而言，我们在关节过剩概率（JEP）和单独的过度渗透率（SEP）标准下得出了可实现的精制渐近学。对于二阶和中度偏离渐近学，我们考虑了两种类型的代码书：球形代码簿，其中每个代码字可以从球体的表面和I.I.D独立均匀地绘制。高斯密码簿中，每个代码字的每个组件都独立于高斯分布绘制。我们在JEP下建立了可实现的二阶速率区域，我们表明，在SEP下，满足轻度力矩条件的任何无内存源都可以连续修复。当专门针对高斯无内存源（GMS）时，我们的结果通过特定的代码设计提供了替代性可实现性证明。我们表明，在JEP和SEP下，相同的中等偏差常数是可以实现的。对于大偏离渐近学，我们仅考虑I.I.D.高斯密码本以来是I.I.D.高斯密码手册的性能比该制度的球形代码簿更好，因为一层不匹配的利率延伸问题（Zhou，Tan，Motani，Tit，2019）。我们得出了JEP和SEP的可实现的指数，并将我们的结果专门用于GM，这似乎是独立兴趣的新结果。
We study the mismatched successive refinement problem where one uses Gaussian codebooks to compress an arbitrary memoryless source with successive minimum Euclidean distance encoding under the quadratic distortion measure. Specifically, we derive achievable refined asymptotics under both the joint excess-distortion probability (JEP) and the separate excess-distortion probabilities (SEP) criteria. For both second-order and moderate deviations asymptotics, we consider two types of codebooks: the spherical codebook where each codeword is drawn independently and uniformly from the surface of a sphere and the i.i.d. Gaussian codebook where each component of each codeword is drawn independently from a Gaussian distribution. We establish the achievable second-order rate-region under JEP and we show that under SEP any memoryless source satisfying mild moment conditions is strongly successively refinable. When specialized to a Gaussian memoryless source (GMS), our results provide an alternative achievability proof with specific code design. We show that under JEP and SEP, the same moderate deviations constant is achievable. For large deviations asymptotics, we only consider the i.i.d. Gaussian codebook since the i.i.d. Gaussian codebook has better performance than the spherical codebook in this regime for the one layer mismatched rate-distortion problem (Zhou, Tan, Motani, TIT, 2019). We derive achievable exponents of both JEP and SEP and specialize our results to a GMS, which appears to be a novel result of independent interest.
