In distributed lossy Gaussian source coding, some correlated sources are observed by isolated encoders, sending index messages to a central decoder.
The decoder requires reconstructing each source with a specific quadratic distortion.  Representing the interaction among the sources with a binary
expansion model, we show that the underlying structure of the problem radically changes when the number of sources exceeds two. Treating each source as
a multi-layer input, it is shown that the layers required by the decoder are combined with some unneeded information, referred as interference.
Therefore, the responsibility of a source coding algorithm is not only to eliminate the redundancy among the inputs, but also to manage the
interference of the sources. It is shown that certain schemes of interference management such as nulling and network coding among the layers can
substantially enhance the achievable schemes and allow us to approximate the rate-distortion region of a many-help-one problem within a bounded gap.
The achievable scheme is developed based on structured (Lattice) codes which provide access to the layers of inputs.