TY - GEN

T1 - Communicating the sum of sources in a 3-sources/3-terminals network

AU - Langberg, Michael

AU - Ramamoorthy, Aditya

PY - 2009

Y1 - 2009

N2 - We consider the network communication scenario in which a number of sources Si each holding independent information Xi wish to communicate the sum σ Xi to a set of terminals tj. In this work we consider directed acyclic graphs with unit capacity edges and independent sources of unit-entropy. The case in which there are only two sources or only two terminals was considered by the work of Ramamoorthy [ISIT 2008] where it was shown that communication is possible if and only if each source terminal pair Si/tj is connected by at least a single path. In this work we study the communication problem in general, and show that even for the case of three sources and three terminals, a single path connecting source/terminal pairs does not suffice to communicate σ Xi. We then present an efficient encoding scheme which enables the communication of σ Xi for the three sources, three terminals case, given that each source terminal pair is connected by two edge disjoint paths. Our encoding scheme includes a structural decom position of the network at hand which may be found useful for other network coding problems as well.

AB - We consider the network communication scenario in which a number of sources Si each holding independent information Xi wish to communicate the sum σ Xi to a set of terminals tj. In this work we consider directed acyclic graphs with unit capacity edges and independent sources of unit-entropy. The case in which there are only two sources or only two terminals was considered by the work of Ramamoorthy [ISIT 2008] where it was shown that communication is possible if and only if each source terminal pair Si/tj is connected by at least a single path. In this work we study the communication problem in general, and show that even for the case of three sources and three terminals, a single path connecting source/terminal pairs does not suffice to communicate σ Xi. We then present an efficient encoding scheme which enables the communication of σ Xi for the three sources, three terminals case, given that each source terminal pair is connected by two edge disjoint paths. Our encoding scheme includes a structural decom position of the network at hand which may be found useful for other network coding problems as well.

UR - http://www.scopus.com/inward/record.url?scp=70449478715&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2009.5205758

DO - 10.1109/ISIT.2009.5205758

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AN - SCOPUS:70449478715

SN - 9781424443130

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2121

EP - 2125

BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009

T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009

Y2 - 28 June 2009 through 3 July 2009

ER -