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On source coding with side information at the decoder

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1 Author(s)

Let{(X_k, Y_k, V_k)}_{k=1}^{infty}be a sequence of independent copies of the triple(X,Y,V)of discrete random variables. We consider the following source coding problem with a side information network. This network has three encoders numbered 0, 1, and 2, the inputs of which are the sequences{ V_k}, {X_k}, and{Y_k}, respectively. The output of encoder i is a binary sequence of rateR_i, i = 0,1,2. There are two decoders, numbered 1 and 2, whose task is to deliver essentially perfect reproductions of the sequences{X_k}and{Y_k}, respectively, to two distinct destinations. Decoder 1 observes the output of encoders 0 and 1, and decoder 2 observes the output of encoders 0 and 2. The sequence{V_k}and its binary encoding (by encoder 0) play the role of side information, which is available to the decoders only. We study the characterization of the family of rate triples(R_0,R_1,R_2)for which this system can deliver essentially perfect reproductions (in the usual Shannon sense) of{X_k}and{Y_k}. The principal result is a characterization of this family via an information-theoretic minimization. Two special cases are of interest. In the first,V = (X, Y)so that the encoding of{V_k }contains common information. In the second,Y equiv 0so that our problem becomes a generalization of the source coding problem with side information studied by Slepian and Wo1f [3].

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Information Theory, IEEE Transactions on  (Volume:21 ,  Issue: 3 )