Can Negligible Rate Increase Network Reliability?

In network cooperation strategies, nodes work together with the aim of increasing transmission rates or reliability. This paper demonstrates that enabling cooperation between the transmitters of a two-user multiple access channel via a cooperation facilitator that has access to both messages results in a network whose maximal- and average-error capacity regions are the same; this benefit ensues even when the information received by each transmitter is negligible. From this result, it follows that if a multiple access channel with no transmitter cooperation has different maximal- and average-error sum-capacities, then the maximal-error sum-capacity of the network consisting of this channel and a cooperation facilitator is not continuous with respect to the output edge capacities of the facilitator. Thus, there exist networks where adding negligible rate yields a non-negligible benefit.

[1]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

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

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

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

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

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

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

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

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

[10]  Michael Langberg,et al.  The unbounded benefit of encoder cooperation for the k-user MAC , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

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

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

[13]  K. Ball.  CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY , 1994 .

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

[15]  Roberto Lucchetti,et al.  Convexity and well-posed problems , 2006 .

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

[17]  Michael Langberg,et al.  Can negligible cooperation increase network reliability? , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[18]  Henry Herng-Jiunn Liao,et al.  Multiple access channels (Ph.D. Thesis abstr.) , 1973, IEEE Trans. Inf. Theory.

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

[20]  Alex J. Grant,et al.  On capacity regions of non-multicast networks , 2010, 2010 IEEE International Symposium on Information Theory.

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

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

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

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