Lossy source coding of multiple Gaussian sources: m-helper problem

We consider the network information theoretic problem of finding the rate distortion bound when multiple correlated Gaussian sources are present. One of these is the source of interest but some side information from other sources is also transmitted to help reduce the distortion in the reproduction of the first source. The other sources are treated as helpers and are also coded. Special cases of this problem have been solved before, such as when the reproduction is lossless, when the sources are conditionally independent given one of them, or when the number of helpers is limited to one. We consider a generalized version and show that the previously derived expressions fall out as special cases of our bound. Our results can be directly utilized by designers to choose not only how many of the available sources should actually be communicated but also which sources have the highest potential to reduce the distortion.