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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 60; no. 9; pp. 5347 - 5374
Main Authors: Chan, Terence H., Grant, Alex
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Description
Summary: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.
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content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2334291