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Quadratic Gaussian source broadcast with individual bandwidth mismatches

We study the problem of broadcasting a Gaussian source over a Gaussian broadcast channel to two users with individual source-channel bandwidth mismatches, under a quadratic distortion measure. Specifically we study the tradeoff between the achievable distortion pairs between the two users. The case when the bandwidth-expansion factors of the two users are identical has been well studied in the literature and to our best knowledge remains an open problem. Surprisingly, when the bandwidth expansion factors are different, we characterize a range of values where both the users simultaneously attain their point-to-point optimal distortion. Furthermore in the high signal-to-noise ratio regime, this set includes nearly all points where the weaker user has the higher bandwidth expansion factor. In other cases, we propose an achievable tradeoff between the distortion pairs.