For Gaussian multiterminal coding at high resolution, the rate gap to centralized coding is conjectured to equal half the sum of squared inverse-covariance off-diagonal terms over pairs never co-encoded, times d squared, and this is verified for up to three sources.
Rate region of the quadratic Gaussian two-encoder source-coding problem,
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Generalized Gaussian Multiterminal Source Coding in the High-Resolution Regime
For Gaussian multiterminal coding at high resolution, the rate gap to centralized coding is conjectured to equal half the sum of squared inverse-covariance off-diagonal terms over pairs never co-encoded, times d squared, and this is verified for up to three sources.