Robust Network Function Computation

We consider the following robust computing problem in a directed acyclic network. A sink node is required to compute with zero error a target function of source messages which are generated at multiple source nodes, whereas the communication links might be corrupted by errors. The nodes in this netw...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 69; no. 11; p. 1
Main Authors: Wei, Hengjia, Xu, Min, Ge, Gennian
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Computation
cut-set bound
Electronic mail
Encoding
Error analysis
Error correction codes
Germanium
Messages
Network coding
network error-correcting codes
Network function computation
Nodes
robust computing capacity
Semantics
Upper bound
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We consider the following robust computing problem in a directed acyclic network. A sink node is required to compute with zero error a target function of source messages which are generated at multiple source nodes, whereas the communication links might be corrupted by errors. The nodes in this network may perform network coding to combat the errors. Given an integer τ, the robust computing rate of a network code against τ errors is the average number of times that the target function can be computed with zero error for one use of the network with at most τ links being corrupted by errors. We derive two cut-set bounds on the robust computing capacity and show that these bounds can be achieved in a multi-edge tree network for computing any target function. Furthermore, we consider linear network codes for computing linear target functions. Given a computing rate, we define a minimum distance to measure the error-tolerant capability of the linear network function computing codes. We propose a Singleton-like bound on this minimum distance and show that this bound is tight in two classes of networks for computing the sum of source messages.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3296154