Localized Dimension Growth: A Convolutional Random Network Coding Approach to Managing Memory and Decoding Delay

Abstract: We consider an \textit{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. 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. We show that this method performs no worse than random linear network codes in terms of decodability, and can provide significant gains in terms of average decoding delay or memory in combination, shuttle and random geometric networks.