The proliferation of mobile devices, such as smartphones or connected objects with rich sensing capabilities, has given rise to a new fast-growing sensing paradigm: mobile crowdsensing. Mobile crowdsensing (MCS) takes advantage of the ubiquity of the devices to process and collect information through voluntary sensing. This paper focuses on one specific issue: decentralized data collection via MCS. 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, or integrating a more complex protocol in order to efficiently identify the sources (participants) and their payloads. This paper presents a novel solution, Network Coding with Random Packet Index Assignment (NeCoRPIA), where packet indices in NC headers are selected in a decentralized way, by simply choosing them randomly. Traditional network decoding techniques apply directly when all original packets have different indices. When this is not the case, 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. Using NeCoRPIA, NC may be performed without coordination between agents. Compared to classical NC, generations of 60 packets may be considered with a header overhead of 66 %, a DRAFT 2 vanishing decoding error probability, and a decoding complexity about 10 times that of Gaussian elimination.