مرکز منطقه ای اطلاع رساني علوم و فناوري - On source coding with side information at the decoder

Abstract :

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 rate $R_i, i = 0,1,2$ . 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, $Y \\equiv 0$ so that our problem becomes a generalization of the source coding problem with side information studied by Slepian and Wo1f [3].