标题： 一种通用的随机编码集合用于逐样本有损压缩 显示英文标题

标题： A Universal Random Coding Ensemble for Sample-wise Lossy Compression

摘要： 我们提出了一种通用的集合，用于随机选择率失真码，该集合在样本意义上是渐近最优的。 根据这个集合，每个再现向量$\hbx$是在与$2^{-LZ(\hbx)}$成比例的概率分布下独立随机选择的，其中$LZ(\hbx)$是与 1978 年版本的 Lempel-Ziv（LZ）算法相关的$\hbx$的码长。 我们证明，在任意失真度量下，该码书以高概率产生一个渐近最优的变速率有损压缩方案，即存在一个对应的逆定理。 根据逆定理，即使解码器提前知道源向量的$\ell$阶类型（$\ell$是一个大但固定的正整数），对于表示同一类型的全部源向量的大多数码字来说，上述码的性能也无法得到实质性的改进。 最后，我们对结果进行了讨论，其中包括与其他编码方案的比较，该方案选择所有与源向量允许失真范围内的向量中 LZ 码长最短的再现向量。 显示英文摘要

摘要： 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.