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In large-scale and dense wireless sensor networks, sensor observations often are correlated and the correlation impacts overall network performance. Another performance limiting factor comes from the non-ideal nature of the wireless links between network nodes. In this paper, we study the detection performance for a distributed detection system with dependent observations under noisy communication channels. In particular, by adopting a novel unified hierarchical independence fusion framework, we derive asymptotic performance limits in terms of error exponents by taking into account the impact of dependent observations and non-ideal channels. The error exponents are investigated under both the Bayesian and the Neyman-Person criteria. Moreover, conditions under which the detection system will result in zero error exponents are also presented in terms of channel capacity requirements.