Can Negligible Cooperation Increase Network Reliability? (Extended Version)

In network cooperation strategies, nodes work together with the aim of increasing transmission rates or reliability. For example, cooperation can be employed to obtain a code with small maximal-error from a code with small average-error that does not make use of cooperation. In networks where rates achievable under a maximal-error constraint differ from those achievable under an average-error constraint, such a benefit can be potentially viewed as both increasing reliability and increasing rate. Let us define the cooperation rate as the number of bits per channel use shared with each node as part of the cooperation strategy. We here demonstrate that even a negligible cooperation rate can sometimes yield a non-negligible benefit. Precisely, we employ Dueck's example of a multiple access channel whose maximal and average-error sum-capacities differ, to show that there exists a network whose maximal-error sum-capacity is not continuous with respect to its edge capacities.

[1]  WeiHsin Gu.  On Achievable Rate Regions for Source Coding over Networks , 2009 .

[2]  Frans M. J. Willems,et al.  The discrete memoryless multiple access channel with partially cooperating encoders , 1983, IEEE Trans. Inf. Theory.

[3]  Michael Langberg,et al.  Network coding: Is zero error always possible? , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[4]  Anand D. Sarwate,et al.  Some observations on limited feedback for multiaccess channels , 2009, 2009 IEEE International Symposium on Information Theory.

[5]  Tracey Ho,et al.  On equivalence between network topologies , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[6]  R. Schneider.  Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

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

[8]  R. Ahlswede.  The Capacity Region of a Channel with Two Senders and Two Receivers , 1974 .

[9]  M. Effros,et al.  A continuity theory for lossless source coding over networks , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

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

[11]  Michael Langberg,et al.  On the Capacity Advantage of a Single Bit , 2016, 2016 IEEE Globecom Workshops (GC Wkshps).

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

[13]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[14]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[15]  Tracey Ho,et al.  On the power of cooperation: Can a little help a lot? , 2014, 2014 IEEE International Symposium on Information Theory.

[16]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

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

[18]  Michelle Effros,et al.  A strong converse for a collection of network source coding problems , 2009, 2009 IEEE International Symposium on Information Theory.

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

[20]  Michael Langberg,et al.  On the cost and benefit of cooperation , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).