On Network Coding for Sum-Networks
DSpace at IIT Bombay
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Title |
On Network Coding for Sum-Networks
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Creator |
RAI, BK
DEY, BK |
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Subject |
Function computation
linear network coding network coding polynomial equations solvability INFORMATION-FLOW MULTICAST CAPACITY |
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Description |
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably) equivalent sum-network for any multiple-unicast network, and thus for any directed acyclic communication network. It is also shown that there exists a linear solvably equivalent multiple-unicast network for every sum-network. It is shown that for any set of polynomials having integer coefficients, there exists a sum-network which is scalar linear solvable over a finite field if and only if the polynomials have a common root in. For any finite or cofinite set of prime numbers, a network is constructed which has a vector linear solution of any length if and only if the characteristic of the alphabet field is in the given set. The insufficiency of linear network coding and unachievability of the network coding capacity are proved for sum-networks by using similar known results for communication networks. Under fractional vector linear network coding, a sum-network and its reverse network are shown to be equivalent. However, under nonlinear coding, it is shown that there exists a solvable sum-network whose reverse network is not solvable.
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Publisher |
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Date |
2014-10-15T12:27:58Z
2014-10-15T12:27:58Z 2012 |
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Type |
Article
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Identifier |
IEEE TRANSACTIONS ON INFORMATION THEORY, 58(1)50-63
http://dx.doi.org/10.1109/TIT.2011.2169532 http://dspace.library.iitb.ac.in/jspui/handle/100/14904 |
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Language |
en
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