## Abstract

We consider the network communication scenario, over directed acyclic networks with unit capacity edges in which a number of sources s_{i} each holding independent unit-entropy information X_{i} wish to communicate the sum sum X_{i} to a set of terminals t_{j}. We show that in the case in which there are only two sources or only two terminals, communication is possible if and only if each source terminal pair s _{i}/t_{j} is connected by at least a single path. For the more general communication problem in which there are three sources and three terminals, we prove that a single path connecting the source terminal pairs does not suffice to communicate sum X_{i}. We then present an efficient encoding scheme which enables the communication of \sum X_{i} for the three sources, three terminals case, given that each source terminal pair is connected by em two edge disjoint paths.

Original language | English |
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Article number | 6481620 |

Pages (from-to) | 655-665 |

Number of pages | 11 |

Journal | IEEE Journal on Selected Areas in Communications |

Volume | 31 |

Issue number | 4 |

DOIs | |

State | Published - 2013 |

## Keywords

- Network coding
- distributed source coding
- function computation
- multicast