In this work, lossy distributed compression of a pair of correlated sources is considered. Conventionally, Shannon's random coding arguments - using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically large - are used to derive achievability results. However, in some multi-terminal communications scenarios, using random codes with constant finite blocklength in certain coding architectures leads to improved achievable regions compared to the conventional approach. In other words, in some network communication scenarios, there is a finite optimal value in the blocklength of the randomly generated code used for distributed processing of information sources. Motivated by this, a coding scheme is proposed which consists of two codebook layers: i) the primary codebook which has constant finite blocklength, and ii) the secondary codebook whose blocklength is taken to be asymptotically large. The achievable performance is analyzed in two steps. In the first step, a characterization of an inner bound to the achievable region is derived in terms information measures which are functions of multi-letter probability distributions. In the next step, a computable single-letter inner-bound to the achievable region is extracted. It is shown through an example that the resulting rate-distortion region is strictly larger than the Berger-Tung achievable region.

中文翻译：

---

分布式源编码的新的可实现率失真区域


在这项工作中，考虑了一对相关源的有损分布式压缩。传统上，香农的随机编码参数 - 使用随机生成的非结构化码本，其块长度被视为渐近大 - 用于导出可实现性结果。然而，在一些多终端通信场景中，与传统方法相比，在某些编码架构中使用具有恒定有限块长度的随机码可以改善可实现的区域。换句话说，在一些网络通信场景中，用于信息源的分布式处理的随机生成码的块长度存在有限的最优值。受此启发，提出了一种由两个码本层组成的编码方案：i）具有恒定的有限块长度的主码本，以及ii）其块长度被视为渐近大的辅助码本。可实现的性能分两个步骤进行分析。在第一步中，根据信息度量导出可实现区域的内部边界的表征，该信息度量是多字母概率分布的函数。在下一步中，提取可实现区域的可计算单字母内界。通过一个例子表明，所得到的率失真区域严格大于Berger-Tung 可实现的区域。