A practical Network Coding and Routing Scheme based on Maximum Flow Combination
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Linear Network CodingLinear Network Coding is a linear combination of packets received at one node into one or more outgoing packets[LiS03]. Assume that there is L bits in each packet, every s sequential bits of a packet forms one symbol over the field F2s with each packet becomes a vector of L/s symbols. Addition and multiplication could be performed over the field F2s. The result encoded packets are in the same length of L. Assume that a number of original packets M1, ... Mn are generated at the source node. In linear network coding, a sequence of coefficients g1, …, gn is picked up from F2s. The encoded packet is  (8)
However, one encoded packet does not carry all the information of the source packets. At the decoding node, sufficient number m (m≥n) of encoded packets and coefficients pairs (g1, X1), …, (gm, Xm) are required in order to recovery the original packets M1, …, Mn. In other words, it is required to solve the m equations and n unknowns.  (9)
In order to solve these equations, the coefficients vectors should be linear independent, i.e. the n×m matrix should be full rank.  (10)
The original packets M1, …, Mn could be works out with the following formula: M=G-1×X (11) Directory: dissertations dissertations -> Second Life on a Mobile Phone Nii Annan September 2011 Dissertation submitted in partial fulfilment for the degree of Master of Science in Information Technology Department of Computing Science and Mathematics University of Stirling dissertations -> Architectures for Controlling an Intelligent Autonomous Vehicle dissertations -> A historical audio and video guidebook for an Android smartphone/tablet John Reid September 2011 Dissertation submitted in partial fulfilment for the degree Download 1.23 Mb. Share with your friends:
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