A curiosity regarding steganographic capacity of pathologically nonstationary sources

Square root laws state that the capacity of an imperfect stegosystem – where the embedding does not preserve the cover distribution exactly – grows with the square root of cover size. Such laws have been demonstrated empirically and proved mathematically for a variety of situations, but not for nonstationary covers. Our aim here is to examine a highly simplified nonstationary source, which can have pathological and unpredictable behaviour. Intuition suggests that, when the cover source distribution is not perfectly known in advance, it should be impossible to distinguish covers and stego objects because the detector can never learn enough information about the varying cover source. However we show a strange phenomenon, whereby it is possible to distinguish stego and cover objects as long as the cover source is stationary for two pixels at a time, and then the capacity follows neither a square root law nor a linear law.