Network Coding Capacity Regions via Entropy Functions

In this paper, we use entropy functions to characterize the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems for acyclic networks. We show that when sources are colocated, the outer bound is tight and the sets of...

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Vydané v:	IEEE transactions on information theory Ročník 60; číslo 9; s. 5347 - 5374
Hlavní autori:	Chan, Terence H., Grant, Alex
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.09.2014 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Applied sciences Coding, codes Decoding Encoding Entropy Error correction & detection Error probability Exact sciences and technology Indexes Information theory Information, signal and communications theory Linear codes Network coding Random variables Routing Secret Signal and communications theory Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Network coding achievable rate regions linearity constraint incremental multicast Packet switching Source coding Error rate Routing Entropy Decoding Data broadcast Information dissemination Multicast Linear code Linear coding Linearity Optimal code Secrecy
ISSN:	0018-9448, 1557-9654
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Popis
Shrnutí:	In this paper, we use entropy functions to characterize the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems for acyclic networks. We show that when sources are colocated, the outer bound is tight and the sets of zero-error achievable and vanishing-error achievable rate-capacity tuples are the same. Then, we extend this paper to networks subject to linear encoding constraints, routing constraints (where some or all nodes can only perform routing), and secrecy constraints. Finally, we show that even for apparently simple networks, design of optimal codes may be difficult. In particular, we prove that for the incremental multicast problem and for the single-source secure network coding problem, characterization of the achievable set can be very hard and linear network codes may not be optimal.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2014.2334291