Consider a generalized multiterminal source coding system, where $\binom{\ell }{ m}$ encoders, each observing a distinct size- $m$ subset of $\ell $ ( $\ell \geq 2$ ) zero-mean unit-variance exchangeable Gaussian sources with correlation coefficient $\rho $ , compress their observations in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate-distortion performance of this system was previously known only for the two extreme cases $m=\ell $ (the centralized case) and $m=1$ (the distributed case), and except when $\rho =0$ , the centralized system can achieve strictly lower compression rates than the distributed system under all non-trivial distortion constraints. Somewhat surprisingly, it is established in the present paper that the optimal rate-distortion performance of the afore-described generalized multiterminal source coding system with $m\geq 2$ coincides with that of the centralized system for all distortions when $\rho \leq 0$ and for distortions below an explicit positive threshold (depending on $m$ ) when $\rho > 0$ . Moreover, when $\rho > 0$ , the minimum achievable rate of generalized multiterminal source coding subject to an arbitrary positive distortion constraint $d$ is shown to be within a finite gap (depending on $m$ and $d$ ) from its centralized counterpart in the large $\ell $ limit except for possibly the critical distortion $d=1-\rho $ .

中文翻译：

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广义高斯多端源编码：对称情况

考虑一个广义的多终端源编码系统，其中 $\binom{\ell }{ m}$ 编码器，每个都观察到不同的大小- 百万美元 的子集 $\ell $ ( $\ell \geq 2$ ) 具有相关系数的零均值单位方差可交换高斯源 $\rho $ ，以这样一种方式压缩他们的观察结果，使得联合解码器可以根据压缩数据在规定的均方误差失真内重建源。该系统的最佳率失真性能以前仅在两种极端情况下为人所知 $m=\ell $ （集中案件）和 $m=1$ （分布式情况），除非 $\rho =0$ ，在所有非平凡失真约束下，集中式系统可以实现严格低于分布式系统的压缩率。有点令人惊讶的是，本文建立了上述广义多端源编码系统的最佳率失真性能 $m\geq 2$ 与所有扭曲的中央系统一致，当 $\rho \leq 0$ 对于低于明确的正阈值的失真（取决于 百万美元 ） 什么时候 $\rho > 0$ . 此外，当 $\rho > 0$ , 受任意正失真约束的广义多端源编码的最小可实现率 $d$ 显示在一个有限的间隙内（取决于 百万美元 和 $d$ ) 来自它在大型中心化的对应物 $\ell $ 除了可能的临界失真之外的限制 $d=1-\rho $ .