Revealing the true achievable rates of scalar Costa scheme

By abandoning the assumption of an infinite document to watermark ratio, we recompute the achievable rates for Egger's scalar Costa scheme (SCS, also known as scalar distortion compensated dither modulation) and show, as opposed to the results reported by Eggers, that the achievable rates of SCS are always larger than those of spread spectrum (SS). Moreover, we show that for small watermark to noise ratios, SCS equivalent to a two-centroid problem, thus revealing interesting relations with SS and with Malvar's improved spread spectrum (ISS). We also show an interesting behavior for the optimal distortion compensation parameter. All these results aim at filling an existing gap in watermarking theory and have important consequences for the design of efficient decoders for data hiding problems.