Incremental multi-hop based on "good" punctured codes and its reliable hop rate

In multi-hop networks, messages are traditionally relayed over a set of sequential point-to-point communication links. An overheard message is typically discarded since the noisy packet is below the detection threshold. However, an overheard packet still contains useful information about the original message, and its consideration can improve the energy efficiency of a transmission scheme. Hence, we study an incremental redundancy multi-hop transmission scheme which enhances the overheard information hop-by-hop. The j-th sequential node combines the previously (over)heard hop transmissions which together form a codeword of a "good" code of rate sufficient for reliable decoding. The analysis of punctured codes whose symbols are distributed over a number of hops is based on a random hop assignment technique. This technique allows for a performance threshold behavior description as a function of the hop rates and a derivation of the asymptotic (as the number of relays goes to infinity) reliable hop rate threshold as a function of channel and mother code parameters. The significant energy savings of the cooperative transmission relative to schemes that discard overheard packets are a function of only the channel parameters.