In many channels, the transmitted signals do not only face noise, but offset mismatch as well. In the prior art, maximum likelihood (ML) decision criteria have already been developed for noisy channels suffering from
signal independent offset
. In this paper, such ML criterion is considered for the case of binary signals suffering from Gaussian noise and
signal dependent offset
. The signal dependency of the offset signifies that it may differ for distinct signal levels, i.e., the offset experienced by the zeroes in a transmitted codeword is not necessarily the same as the offset for the ones. Besides the ML criterion itself, also an option to reduce the complexity is considered. Further, a brief performance analysis is provided, confirming the superiority of the newly developed ML decoder over classical decoders based on the Euclidean or Pearson distances.