The design of source decoders that employ the residual redundancy at the source coder output is an interesting research direction in the joint source channel coding framework. Such decoders are expected to replace the traditionally heuristic error concealment units that are elements of most multimedia communication systems. In this work, we consider the reconstruction of signals encoded with a multi-stage vector quantizer (MSVQ) and transmitted over a noisy channel. The MSVQ maintains a moderate complexity and, due to its successive refinement feature, is a suitable choice for the design of layered (progressive) source codes. An approximate MMSE source decoder for MSVQ is presented and its application to reconstruction of LPC parameters in MELP is analyzed. Numerical results demonstrates the effectiveness of the proposed schemes.