A recently developed theory suggests that network coding is a generalization of source coding and channel coding and thus yields a significant performance improvement in terms of throughput and spatial diversity. This paper proposes a cooperative design of a parity-check network coding scheme in the context of a two-source multiple access relay channel (MARC) model, a common compact model in hierarchical wireless sensor networks (WSNs). The scheme uses Low-Density Parity-Check (LDPC) as the surrogate to build up a layered structure which encapsulates the multiple constituent LDPC codes in the source and relay nodes. Specifically, the relay node decodes the messages from two sources, which are used to generate extra parity-check bits by a random network coding procedure to fill up the rate gap between Source-Relay and Source-Destination transmissions. Then, we derived the key algebraic relationships among multidimensional LDPC constituent codes as one of the constraints for code profile optimization. These extra check bits are sent to the destination to realize a cooperative diversity as well as to approach MARC decode-and-forward (DF) capacity.
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