论文标题
用于样本有损压缩的通用随机编码集合
A Universal Random Coding Ensemble for Sample-wise Lossy Compression
论文作者
论文摘要
我们提出了一个通用集合，用于随机选择速率限制代码，在样本方面，该集合在样本方面是最佳的。根据这个合奏，每个复制向量$ \ hbx $在概率分布中以与$ 2^{ - lz（\ hbx）} $成比例的分布方式进行独立选择，其中$ lz（\ hbx）$是$ \ hbx的代码长度与1978年的lempel-ziv（lempel-ziv（Lempel-Ziv）相关。我们表明，在很高的概率上，在任意失真度量下，产生的代码簿产生了渐近的最佳可变速率损耗压缩方案，从某种意义上说，匹配的匡威定理也成立。根据Converse定理，即使解码器知道$ \ ell $ ther $ ther订单的源源向量（$ \ ell $是一个大但固定的正整数），上述代码的性能本质上就无法得到改善，对于绝大多数代表所有源代表所有源代表的代码量都代表所有类型的代码。最后，我们提供了有关结果的讨论，其中包括与编码方案的比较，该方案选择了在从源向量中允许失真范围内的所有向量中选择最短LZ代码长度的复制向量。
We propose a universal ensemble for random selection of rate-distortion codes, which is asymptotically optimal in a sample-wise sense. According to this ensemble, each reproduction vector, $\hbx$, is selected independently at random under the probability distribution that is proportional to $2^{-LZ(\hbx)}$, where $LZ(\hbx)$ is the code-length of $\hbx$ pertaining to the 1978 version of the Lempel-Ziv (LZ) algorithm. We show that, with high probability, the resulting codebook gives rise to an asymptotically optimal variable-rate lossy compression scheme under an arbitrary distortion measure, in the sense that a matching converse theorem also holds. According to the converse theorem, even if the decoder knew $\ell$-th order type of source vector in advance ($\ell$ being a large but fixed positive integer), the performance of the above-mentioned code could not have been improved essentially, for the vast majority of codewords that represent all source vectors in the same type. Finally, we provide a discussion of our results, which includes, among other things, a comparison to a coding scheme that selects the reproduction vector with the shortest LZ code length among all vectors that are within the allowed distortion from the source vector.
