A few meta-theorems in network information theory

This paper reviews the relationship among several notions of capacity regions of a general discrete memoryless network under different code classes and performance criteria, such as average vs. maximal or block vs. bit error probabilities and deterministic vs. randomized codes. Applications of these meta-theorems include several structural results on capacity regions and a simple proof of the network equivalence theorem.

[1]  A. Winter Compression of sources of probability distributions and density operators , 2002, quant-ph/0208131.

[2]  Thomas M. Cover,et al.  Network Information Theory , 2001 .

[3]  Abbas El Gamal,et al.  Network Information Theory , 2021, 2021 IEEE 3rd International Conference on Advanced Trends in Information Theory (ATIT).

[4]  Ning Cai The Maximum Error Probability Criterion, Random Encoder, and Feedback, in Multiple Input Channels , 2014, Entropy.

[5]  Peter W. Shor,et al.  Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem , 2001, IEEE Trans. Inf. Theory.

[6]  Suhas N. Diggavi,et al.  Optimality and Approximate Optimality of Source-Channel Separation in Networks , 2010, IEEE Transactions on Information Theory.

[7]  Andreas J. Winter,et al.  Quantum Reverse Shannon Theorem , 2009, ArXiv.

[8]  Muriel Médard,et al.  A Theory of Network Equivalence— Part I: Point-to-Point Channels , 2011, IEEE Transactions on Information Theory.

[9]  G. David Forney,et al.  Concatenated codes , 2009, Scholarpedia.

[10]  Shirin Jalali,et al.  On the separation of lossy source-network coding and channel coding in wireline networks , 2010, 2010 IEEE International Symposium on Information Theory.

[11]  Paul W. Cuff,et al.  Distributed Channel Synthesis , 2012, IEEE Transactions on Information Theory.

[12]  Andreas J. Winter,et al.  The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels , 2009, IEEE Transactions on Information Theory.

[13]  Haim H. Permuter,et al.  Coordination Capacity , 2009, IEEE Transactions on Information Theory.

[14]  F. Willems The maximal-error and average-error capacity region of the broadcast channel are identical : A direct proof , 1990 .

[15]  Tracey Ho,et al.  On the impact of a single edge on the network coding capacity , 2011, 2011 Information Theory and Applications Workshop.

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

[17]  Lihua Song,et al.  A separation theorem for single-source network coding , 2006, IEEE Transactions on Information Theory.

[18]  Imre Csiszár,et al.  Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition , 2011 .