Tunable sparse network coding (TSNC) with various sparsity levels of the coded packets and different feedback mechanisms is analysed in the context of data gathering applications in multi-hop networks. The goal is to minimize the completion time, i.e., the total time required to collect all data packets from the nodes while maintaining the per packet overhead at a minimum.

We exploit two types of feedback: (1) the explicit feedback sent deliberately between nodes and (2) the implicit feedback emerged when a node hears its neighbour transmissions. Analytical bounds for a line network are derived using a fluid model, which is valid for any field size, various sparsity levels and the aforesaid feedback mechanisms. Our results show that implicit and explicit feedback mechanisms are instrumental in reducing the completion time for sparse codes.

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