The supremum sum-rate loss of quadratic Gaussian direct multiterminal source coding

Wagner et al. recently characterized the rate region for the quadratic Gaussian two-terminal source coding problem. They also show that the Berger-Tung sum-rate bound is tight in the symmetric case, where all sources are positively symmetric and all target distortions are equal. This work studies the sum-rate loss of quadratic Gaussian direct multiterminal source coding. We first give the minimum sum-rate for joint encoding of Gaussian sources in the symmetric case, we than show that the supremum of the sum-rate loss due to distributed encoding in this case is 1/2 log2 5/4 = 0.161 b/s when L = 2 and increases in the order of radic(L)/2 log2 e b/s as the number of terminals L goes to infinity. The supremum sum-rate loss of 0.161 b/s in the symmetric case equals to that in general quadratic Gaussian two-terminal source coding without the symmetric assumption. It is conjectured that this equality holds for any number of terminals.