This paper considers data collection using a network of uncoordinated, heterogeneous, and possibly mobile devices. Using medium and short-range radio technologies, multi-hop communication is required to deliver data to some sink. While numerous techniques from managed networks can be adapted, one of the most efficient (from the energy and spectrum use perspective) is network coding (NC). NC is well suited to networks with mobility and unreliability, however, practical NC requires a precise identification of individual packets that have been mixed together. In a purely decentralized system, this requires either conveying identifiers in headers along with coded information as in COPE, or integrating a more complex protocol in order to efficiently identify the sources (participants) and their payloads. A novel solution, Network Coding with Random Packet Index Assignment (NeCoRPIA), is presented where packet indices in NC headers are selected in a decentralized way, by choosing them randomly. Traditional network decoding can be applied when all original packets have different indices. When this is not the case, \emph{i.e.}, in case of collisions of indices, a specific decoding algorithm is proposed. A theoretical analysis of its performance in terms of complexity and decoding error probability is described. Simulation results match well the theoretical results. Comparisons of NeCoRPIA header lengths with those of a COPE-based NC protocol are also provided.