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This paper addresses the problem of efficient data gathering in wireless sensor networks with a complexity constrained data gathering node. A particular scenario of interest is a cluster of sensor nodes among which one is selected as the cluster head. Distributed source coding allows for exploiting the dependency between the nodes observations and reducing the required rate of communications. We consider a rate allocation structure, which incorporates the decoder complexity constraints, by limiting the number of nodes whose data may be stored and exploited during decoding. Based on this structure, we investigate the problem of rate allocation for the nodes to minimize the total cost, where the cost of a node is a general function of its rate and related parameters. To this end, an optimal dynamic programming solution based on a trellis structure is proposed. Also, a suboptimal yet high performance solution is presented whose complexity grows in polynomial order as the number of network nodes increases. Numerical results demonstrate that the proposed solutions, even with limited complexity, allow for exploiting most of the available dependency and hence the achievable compression gain.