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...conclusion. As a remark, even if we allow an arbitrarily small probability of decoding error in the usual Shannon sense, by modifying our proof by means of a standard application of Fano’s inequality =-=[2]-=-, it can be seen that it is still necessary for the value of a max-flow from to , to be greater than or equal to . The details are omitted here. V. ADMISSIBILITY In this section, we prove that . In Se...

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...lso, we can ask under what condition can optimality be achieved without network coding. These are interesting problems for further research. Recently, there has been a lot of interest in factor graph =-=[7]-=-, a graphical model which subsumes Markov random field, Bayesian network, and Tanner graph. In particular, the problem of representing codes in graphs [11], [6] has received much attention. The codes ...

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...rk along this line [12], [8], [14] into a new direction in multiterminal source coding. In the past, most results in multiterminal source coding are generalizations of either the Slepian–Wolf problem =-=[9]-=- or the multiple descriptions problem [3]. The class of problems we have proposed are generalizations of neither of these problems. Further, they distinguish themselves from most classical multitermin...

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...single-source problem, there are still many unresolved issues which are worth further investigation. In proving our result for acyclic graphs, we have used a random block code. Recently, Li and Yeung =-=[4]-=- have devised a systematic procedure to construct linear codes for acyclic networks. Along another line, the example in Section V shows that convolutional codes are good alternatives to block codes. I...

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... new direction in multiterminal source coding. In the past, most results in multiterminal source coding are generalizations of either the Slepian–Wolf problem [9] or the multiple descriptions problem =-=[3]-=-. The class of problems we have proposed are generalizations of neither of these problems. Further, they distinguish themselves from most classical multiterminal source coding problems in the followin...

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...re has been a lot of interest in factor graph [7], a graphical model which subsumes Markov random field, Bayesian network, and Tanner graph. In particular, the problem of representing codes in graphs =-=[11]-=-, [6] has received much attention. The codes we construct for a given network in this paper can be regarded as a special type of codes in a graph. APPENDIX PROBABILISTIC CODING DOES NOT IMPROVE PERFOR...

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... values of a max-flow from to are greater than or equal to , the rate of the information source. The spirit of our conjecture resembles that of the celebrated Max-flow Min-cut Theorem in graph theory =-=[1]-=-. Before we end this section, we give a few examples to illustrate our conjecture. We first illustrate by the example in Fig. 5 that the conjecture is true for . Fig. 5(a) shows the capacity of each e...

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...accessible by this decoder is at least . Thus the conditions are necessary for (1) (2) (3) (4) to be admissible. On the other hand, these conditions are seen to be sufficient by the work of Singleton =-=[10]-=- (also cf. [12]). We now give a graph-theoretic interpretation of the above result. The graph corresponding to the system in Fig. 3 is given in Fig. 4, where we use to label the source and to label a ...

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...ssible coding rate region , i.e., the set of all admissible , for any graph and multicast requirements and . The model we have described includes both multilevel diversity coding (without distortion) =-=[12]-=-, [8], [13] and distributed source coding [14] as special cases. As an illustration, let us show how the multilevel diversity coding system in Fig. 1 can be formulated as a special case of our model. ...

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... coding rate region , i.e., the set of all admissible , for any graph and multicast requirements and . The model we have described includes both multilevel diversity coding (without distortion) [12], =-=[8]-=-, [13] and distributed source coding [14] as special cases. As an illustration, let us show how the multilevel diversity coding system in Fig. 1 can be formulated as a special case of our model. In th...

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...not be decomposed into two sets of subrates as prescribed above. Therefore, coding by superposition is not optimal in general, even when the two information sources are generated at the same node. In =-=[5]-=-, 1 it was found that coding by superposition is optimal for 86 out of all 100 configurations of multilevel diversity coding systems with three encoders. In [8] and [13] it was shown that coding by su...

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... been a lot of interest in factor graph [7], a graphical model which subsumes Markov random field, Bayesian network, and Tanner graph. In particular, the problem of representing codes in graphs [11], =-=[6]-=- has received much attention. The codes we construct for a given network in this paper can be regarded as a special type of codes in a graph. APPENDIX PROBABILISTIC CODING DOES NOT IMPROVE PERFORMANCE...

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...ll admissible , for any graph and multicast requirements and . The model we have described includes both multilevel diversity coding (without distortion) [12], [8], [13] and distributed source coding =-=[14]-=- as special cases. As an illustration, let us show how the multilevel diversity coding system in Fig. 1 can be formulated as a special case of our model. In this system, there are two sources, and . D...