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In this paper, we address the problem of extending the lifetime of sensor nodes, in particular those that are located close to the base station, using a new parity forwarding technique. The parity-forwarding refers to a relaying strategy in which a relay node sends a parity of the decoded codeword to facilitate transmission by other nodes. In this scheme, the relay completely decodes the transmitted codeword but only forwards a parity symbol to the destination, which reduces the encoding complexity and bandwidth/power expenditures at the relay. It is shown that this strategy achieves the capacity of a new class of single source, single destination, degraded two- relay networks by Razaghi, P. and Yu, W. (2006).