Near tightness of the El Gamal and Cover region for two descriptions

We give a single letter outer bound for the two descriptions problem for iid sources that is universally close to the El Gamal and Cover (EGC) inner bound. The gaps in the quadratic distortion case for the sum and individual rates are upper bounded by 1.5 and 0.5 bits/sample, respectively. These constant bounds are universal with respect to the source being encoded, provided that its variance is finite. They are also universal with respect to the desired distortion levels, under the assumption that, after normalizing the source to have unit variance, D_i ∈ (0,1) for i ∈ {0,1,2} and D₀ ≤ (D₁^-1 + D₂^-1 - 1)^-1.