Robustness of iterative decoders, i.e., their ability to successfully decode the received signal in spite of unknown changes in the channel parameter, is investigated. More specifically, using low-density parity-check codes and iterative message-passing decoders for error correction, we consider reliable communication over a binary-input power-limited Gaussian channel whose noise power is not perfectly known to the receiver. We propose iterative algorithms that can decode the received signal in the presence of a strong uncertainty in the channel parameter. Such decoders are of interest for wireless applications, where the channel attenuation could significantly vary with time