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Average log-likelihood ratios (LLRs) constitute sufficient statistics for centralized maximum-likelihood block decoding as well as for a posteriori probability evaluation which enables bit-wise (possibly iterative) decoding. By acquiring such average LLRs per sensor it becomes possible to perform these decoding tasks in a low-complexity distributed fashion using wireless sensor networks. At affordable communication overhead, the resultant distributed decoders rely on local message exchanges among single-hop neighboring sensors to achieve iteratively consensus on the average LLRs per sensor. Furthermore, the decoders exhibit robustness to non-ideal inter-sensor links affected by additive noise and random link failures. Pairwise error probability bounds benchmark the decoding performance as a function of the number of consensus iterations. Interestingly, simulated tests corroborating the analytical findings demonstrate that only a few consensus iterations suffice for the novel distributed decoders to approach the performance of their centralized counterparts.