Interference neutralization in distributed lossy source coding

We consider a problem of distributed lossy Gaussian source coding with inputs (y₁, y₂, y₃), where y₁ and y₂ are positively correlated, y₃ = y₁ - cy₂, c ≥ 0, and the decoder requires y₃ with a target distortion. For this problem, known achievable schemes are unboundedly loose. Inspired by results of binary expansion models, we characterize the rate-distortion region within a bounded gap. Treating each source as a multilayer input, an achievable scheme is developed based on the following observations: (i) some middle layers of y₁ and y₂ are not needed at the decoder, (ii) the required layers are combined with some unneeded interference information, (iii) linear operations among input layers can unboundedly reduce the load of reporting interference. Showing that the cut-set outer-bound has an unbounded gap, we also establish a new outer-bound to prove the bounded-gap result.