Bavirisetti, Teja Damodaram and Ganesan, Abhinav and Prasad, K and Rajan, Sundar B
(2012)
*A transform approach to linear network coding for acyclic networks with delay.*
In: 2012 IEEE International Symposium on Information Theory Proceedings (ISIT), 1-6 July 2012, Cambridge, MA.

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## Abstract

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Item Type: | Conference Paper |
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Publisher: | IEEE |

Additional Information: | Copyright of this article belongs to IEEE. |

Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |

Date Deposited: | 13 Dec 2013 15:20 |

Last Modified: | 27 Feb 2019 05:24 |

URI: | http://eprints.iisc.ac.in/id/eprint/47925 |

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