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When correlated sources are to be communicated over a network to more than one sink, joint source-network coding is, in general, required for information theoretically optimal transmission. Whereas on the encoder side simple randomized schemes based on linear codes suffice, the decoder is required to perform joint source-network decoding which is computationally expensive. Focusing on maximum a-posteriori decoders (or, in the case of continuous sources, conditional mean estimators), the authors show how to exploit (structural) knowledge about the network topology as well as the source correlations giving rise to an efficient decoder implementation (in some cases even with linear dependency on the number of nodes).
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