A separation theorem for single-source network coding

In this paper, we consider a point-to-point communication network of discrete memoryless channels. In the network, there are a source node and possibly more than one sink node. Information is generated at the source node and is multicast to each sink node. We allow a node to encode its received information before loading it onto an outgoing channel, where the channels are independent of each other. We also allow the nodes to pass along messages asynchronously. In this paper, we characterize the admissibility of single-source multi-sink communication networks. Our result can be regarded as a network generalization of Shannon's result that feedback does not increase the capacity of a discrete memoryless channels (DMCs), and it implies a separation theorem for network coding and channel coding in such a communication network.

[1]  M. Vetterli,et al.  On the asymptotic capacity of Gaussian relay networks , 2002, Proceedings IEEE International Symposium on Information Theory,.

[2]  R. Gallager,et al.  The Gaussian parallel relay network , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[3]  James L. Massey,et al.  Conservation of mutual and directed information , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[4]  Zhen Zhang,et al.  Distributed Source Coding for Satellite Communications , 1999, IEEE Trans. Inf. Theory.

[5]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[6]  Muriel Médard,et al.  An algebraic approach to network coding , 2003, TNET.

[7]  van der MeulenE..  A Survey of Multi-Way Channels in Information Theory: , 1977 .

[8]  Michael Gastpar,et al.  The multiple-relay channel: coding and antenna-clustering capacity , 2002, Proceedings IEEE International Symposium on Information Theory,.

[9]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[10]  Jack K. Wolf,et al.  The capacity region of a multiple-access discrete memoryless channel can increase with feedback (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[11]  Edward C. van der Meulen,et al.  A survey of multi-way channels in information theory: 1961-1976 , 1977, IEEE Trans. Inf. Theory.

[12]  Raymond W. Yeung,et al.  Symmetrical multilevel diversity coding , 1997, IEEE Trans. Inf. Theory.

[13]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[14]  A. Sridharan.  Broadcast Channels , 2022 .

[15]  Cyril Leung,et al.  An achievable rate region for the multiple-access channel with feedback , 1981, IEEE Trans. Inf. Theory.

[16]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[17]  S. Borade.  Network information flow: limits and achievability , 2002, Proceedings IEEE International Symposium on Information Theory,.

[18]  Claude E. Shannon,et al.  The zero error capacity of a noisy channel , 1956, IRE Trans. Inf. Theory.

[19]  Thomas M. Cover,et al.  An achievable rate region for the broadcast channel , 1975, IEEE Trans. Inf. Theory.

[20]  Rudolf Ahlswede,et al.  Multi-way communication channels , 1973 .

[21]  Raymond W. Yeung,et al.  A First Course in Information Theory , 2002 .

[22]  Te Sun Han,et al.  Slepian-Wolf-Cover Theorem for Networks of Channels , 1980, Inf. Control..

[23]  Jacob Wolfowitz,et al.  Multiple Access Channels , 1978 .

[24]  J. Massey.  CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

[25]  Lihua Song,et al.  Zero-error network coding for acyclic network , 2003, IEEE Trans. Inf. Theory.

[26]  Gerhard Kramer.  Capacity results for the discrete memoryless network , 2003, IEEE Trans. Inf. Theory.