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The authors consider an Adaptive Random Convolutional Network Coding (ARCNC) algorithm to address the issue of field size in random network coding for multicast, and study its memory and decoding delay performances through both analysis and numerical simulations. ARCNC operates as a convolutional code, with the coefficients of local encoding kernels chosen randomly over a small finite field. The cardinality of local encoding kernels increases with time until the global encoding kernel matrices at related sink nodes have full rank. ARCNC adapts to unknown network topologies without prior knowledge, by locally incrementing the dimensionality of the convolutional code.
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