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Generalized Gaussian Multiterminal Source Coding: The Symmetric Case

机译：广义高斯多体源编码：对称情况

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摘要

Consider a generalized multiterminal source coding system, where ((l)(m)) encoders, each observing a distinct sizem subset of l (l >= 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 = l (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 = 2 coincides with that of the centralized system for all distortions when rho <= 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 l limit except for possibly the critical distortion d = 1-rho.
机译：考虑一般化的多特源编码系统，其中（（L）（m））编码器，每个编码器，每个观察L（l> = 2）零平均单位 - 方差交换的高斯源的不同的Sizem子集，具有相关系数Rho，压缩它们的观察以这样的方式，联合解码器可以基于压缩数据重建规定的平均误差失真内的源。此系统的最佳速率 - 失真性能以前仅为两个极端情况M = L（集中式外壳）和M = 1（分布式外壳），并且除了rho = 0时，集中式系统可以严格降低压缩率比在所有非级别失真约束下的分布式系统。有些令人惊讶的是，在本文中建立了上述广义多字节源编码系统的最佳速率失真性能，其中具有M = 2的集中系统的曲线恰逢rho <= 0的所有扭曲以及下面的畸变。当rho> 0时，显式正阈值（取决于m）。此外，当rho> 0时，经过任意正畸约束d的广义多态源编码的最小可实现的速率被显示为有限间隙（取决于m除了可能的临界失真d = 1-rho之外，它在大l限制中的集中对应物。

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