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In this paper, we show how the Gaussian mixture modeling framework used to develop efficient source encoding schemes can be further exploited to model source statistics during channel decoding in an iterative framework to develop an effective joint source-channel decoding scheme. The joint probability density function (PDF) of successive source frames is modeled as a Gaussian mixture model (GMM). Based on previous work, the marginal source statistics provided by the GMM is used at the encoder to design a low-complexity memoryless source encoding scheme. The source encoding scheme has the specific advantage of providing good estimates to the probability of occurrence of a given source code-point based on the GMM. The proposed iterative decoding procedure works with any channel code whose decoder can implement the soft-output Viterbi algorithm that uses a priori information (APRI-SOVA) or the BCJR algorithm to provide extrinsic information on each source encoded bit. The source decoder uses the GMM model and the channel decoder output to provide a priori information back to the channel decoder. Decoding is done in an iterative manner by trading extrinsic information between the source and channel decoders. Experimental results showing improved decoding performance are provided in the application of speech spectrum parameter compression and communication.