The robustness property can be added to DSC system at the expense of reducing performance, i.e., increasing the sum-rate. The aim of designing robust DSC schemes is to trade off between system robustness and compression efficiency. In this paper, after deriving an inner bound on the rate–distortion region for the quadratic Gaussian MDC based RDSC system with two encoders, the structure of the RDSC system with three encoders and more generally with an arbitrary number of encoders are considered. Then inner bounds on the rate–distortion region for both MDC and MLC based Gaussian RDSC systems with an arbitrary number of encoders are derived. Finally, a practical coding approach for both MDC and MLC based Gaussian RDSC systems with an arbitrary number of encoders is proposed. The proposed approach is based on the multilevel Slepian-Wolf coded quantization framework. The approach is applied on the systems with two and three encoders and then extending and applying the approach on the systems with the number of encoders greater than three is straightforward. The obtained results are promising and satisfy the inner bounds for both rates and distortions for both sides and central decoders. This work paves the way of practical RDSC design in a general case.