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We consider the distributed estimation by a network consisting of a fusion center and a set of sensor nodes, where the goal is to maximize the network lifetime, defined as the estimation task cycles accomplished before the network becomes nonfunctional. In energy-limited wireless sensor networks, both local quantization and multihop transmission are essential to save transmission energy and thus prolong the network lifetime. The network lifetime optimization problem includes three components: i) optimizing source coding at each sensor node, ii) optimizing source throughput of each sensor node, and iii) optimizing multihop routing path. Fortunately, source coding optimization can be decoupled from source throughput and multihop routing path optimization, and is solved by introducing a concept of equivalent 1-bit MSE function. Based on the optimal source coding, the source throughput and multihop routing path optimization is formulated as a linear programming (LP) problem, which suggests a new notion of character-based routing. The proposed algorithm is optimal and the simulation results show that a significant gain is achieved by the proposed algorithm compared with heuristic methods.