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Localized Dimension Growth in Random Network Coding: A Convolutional Approach
We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)
algorithm to address the issue of field size in random network coding. ARCNC
operates as a convolutional code, with the coefficients of local encoding
kernels chosen randomly over a small finite field. The lengths of local
encoding kernels increase with time until the global encoding kernel matrices
at related sink nodes all have full rank. Instead of estimating the necessary
field size a priori, ARCNC operates in a small finite field. It adapts to
unknown network topologies without prior knowledge, by locally incrementing the
dimensionality of the convolutional code. Because convolutional codes of
different constraint lengths can coexist in different portions of the network,
reductions in decoding delay and memory overheads can be achieved with ARCNC.
We show through analysis that this method performs no worse than random linear
network codes in general networks, and can provide significant gains in terms
of average decoding delay in combination networks.Comment: 7 pages, 1 figure, submitted to IEEE ISIT 201
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