Source requantization: successive degradation and bit stealing

We consider source requantization in two forms - successive degradation (i.e., source fidelity reduction) and bit stealing (i.e., information embedding) when no forward planning has been done to facilitate the requantization. We focus on finite-alphabet sources with arbitrary distortion measures as well as the Gaussian-quadratic scenario. For the successive degradation problem, we show an achievable distortion-rate trade-off for non-hierarchically structured rate-distortion achieving codes, and compare it to the distortion-rate trade-off of successively refinable codes. We further consider source requantization in the form of bit stealing, whereby an information embedder acts on a quantized source, producing an output at the same rate. Building on the successive degradation results, we develop achievable distortion-rate trade-offs. Two cases are considered, corresponding to whether the source decoder is informed of any bit stealing or not. In the latter case, the embedder must produce outputs in the original source codebook. For the Gaussian-quadratic scenario, all trade-offs are within 0.5 bits/sample of the distortion-rate bound. Furthermore, for bit stealing, the use of simple post-reconstruction processing that is only a function of the embedded rate can eliminate the loss experienced by uninformed decoders.