On Two-Stage Sequential Coding of Correlated Sources

We study the problem of two-stage sequential coding (TSSC), which is an extension of sequential coding of correlated sources. Let X and Y be dependent random variables. The network contains two encoders and two decoders: 1) a Y encoder with input Y; 2) an X encoder with inputs X and Y; 3) a Y decoder that reconstructs Y; and 4) an X decoder that reconstructs X. The first stage is traditional sequential coding, where the Y encoder describes Y to both the X decoder and Y decoder, and the X encoder describes X and Y to the X decoder. At the second stage, the Y encoder refines the description of Y, and the X encoder refines the description of X. The TSSC model is a theoretical abstraction of scalable video coding; here, Y and X represent successive frames of a video sequence, and the two stages together give an embedded description that allows the video to be decoded at two distinct rates. We give an inner bound on the rate distortion region for this TSSC model. The tight bound on the rate distortion region is derived when Y must be reconstructed losslessly (in the usual Shannon sense) in the second stage. We also study the minimum total rate of the TSSC model and show that the minimum total rate of one-stage sequential coding cannot be achieved at both stages for jointly Gaussian sources. This theoretical result can shed light on the rate-distortion performance behavior of scalable video coding widely noted by practitioners.