Comments on Cut-Set Bounds on Network Function Computation

A function computation problem over a directed acyclic network has been considered in the literature, where a sink node is required to compute a target function correctly with the inputs arbitrarily generated at multiple source nodes. The network links are error free but capacity limited, and the in...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 64; no. 9; pp. 6454 - 6459
Main Authors: Huang, Cupjin, Tan, Zihan, Yang, Shenghao, Guang, Xuan
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Computation
Computational modeling
computing capacity
Electronic mail
Encoding
general cut-set bound
information theory
Integrated circuits
Network coding
Network function computation
Nodes
tightness
Upper bound
Upper bounds
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:A function computation problem over a directed acyclic network has been considered in the literature, where a sink node is required to compute a target function correctly with the inputs arbitrarily generated at multiple source nodes. The network links are error free but capacity limited, and the intermediate nodes perform network coding. The computing rate of a network code is the average number of times that the target function is computed for one use of the network, i.e., each link in the network is used at most once. In the existing papers, two cut-set bounds were proposed on the computing rate. However, we in this paper show that these bounds are not valid for general network function computation problems. We analyze the reason of the invalidity and propose a general cut-set bound by using a new equivalence relation associated with the inputs of the target function. Moreover, some results in the existing papers were proved by applying the invalid upper bound. We also justify the validity of these results.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2018.2827405