In wireless sensor networks, due to the bandwidth constraint, the distributed nodes (DNs) might only provide binary representatives of the source signal, and then transmit them to the central node (CN). In this paper, we consider the joint estimation of signal amplitude and background noise variance from binary observations over decentralized channels. We first analyze the Cramér-Rao lower bounds (CRLBs) of the parameters of interest and develop a quasilinear estimator (QLE), in which the desirable estimates can be obtained from several intermediate parameters linearly. Next, we consider a more realistic situation where the decentralized channel is noisy during the data transmission. Based on the error propagation model, the asymptotic analysis shows that the performance of the proposed QLE is mainly dominated by the thresholds of the quantizers, which encourages us to adopt a correlated quantization (CQ) scheme by exploiting the spatial correlation among background noises/channel noises. To ease the implementation of QLE in practice, an adaptive quantization (AQ) scheme is also proposed so as to obtain reasonable selections of the required thresholds. Finally, numerical simulations are provided to validate our theoretical findings.