Network coding theory via commutative algebra
主 题: Network coding theory via commutative algebra
报告人: 李硕彦(Bob Li) (香港中文大學 訊息工程講座教授)
时 间: 2009-06-15 上午10:20 - 12:00
地 点: 资源大厦1328
The conventional theory of network coding (NC) is restricted to acyclic networks, but practical applications are not. This is because the unidirectional nature of time allows the time-multiplexed deployment of a cyclic network to be unfolded into an acyclic trellis network in the combined space-time domain. Thus linear NC theory is extended to convolutional NC, where the data is not a symbol but rather a rational power series over the symbol field. However, practical applications of convolutional NC are hindered by the difficulty in precise inter-node synchronization. Adopting data units belonging to a discrete valuation ring (DVR) in general, much of the network coding theory extends to cyclic networks. Generality enhances the potential of applicability. For example, if the uniformizer of the DVR represents a shift in any domain other than time, then the DVR-based NC is insensitive to imprecise inter-node synchronization.
Besides the treatise in commutative algebra, we also explore the efficiency issue of code construction. Given a network, a quadratically large acyclic network is constructed so that every optimal code on the acyclic network subject to some straightforward restriction induces an optimal code on the given network. In this way, existing construction algorithms over acyclic networks can be adapted for cyclic networks as well.