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This paper presents the Simple Packet Combining (SPaC) error-correction scheme for wireless sensor networks. Nodes buffer corrupt packets, and when two or more corrupt versions of a packet have been received, a packet combining procedure attempts to recover the original packet from the corrupt copies. Packet combining exploits the broadcast medium and spatial diversity of a multi-hop wireless network by using packets overheard at any node, in addition to the next-hop destination of the packet itself. Unlike point-to-point forward error correction (FEC), packet combining therefore helps multi-node interactions such as multi-hop routing or broadcasting as well as to hop-by-hop communication. Also, SPaC does not transmit redundant overhead on good links and does not require costly probes to estimate channel conditions. We have implemented SPaC as a link-layer extension on sensor nodes; it is transparent to upper layer protocols and has low memory and CPU footprints. We evaluate performance through a combination of analysis, trace-driven simulation, indoor and outdoor testbed micro-benchmarks, and deployment on a live network. The results show significant performance gains, even when accounting for the energy cost of CPU processing. We also present detailed bit-level link measurements and the design and evaluation of a new preamble detection scheme motivated by these measurements.