Effect of noise and entropy
According to the link you provided: 

$H(error) = H(y-\hat{y}) = H(Var[y]+Var[\hat{y}])$. While $Var[y]$ decreases with increasing of SNR, $Var[\hat{y}]$ stays the same (because it's not dependent of the noise, it depends on the signal alphabet only). So we may guess $H(error)$ decreases with increasing of SNR.