On Multi-Stage Sequential Coding of Correlated Sources

We study the problem of multi-stage sequential coding (MSSC), which is an extension of sequential coding of correlated sources. Consider two correlated random variables $X$ and $Y$ to be coded in two stages. The first stage is sequential coding as referred to in the existing literature. At the second stage, the $Y$ encoder refines the information of $Y$ without any knowledge of $X$, and $X$ encoder refines the information of $X$ with the knowledge of $Y$, while all previous outputs are known at the decoder. As the sequential coding problem provides a theoretical abstraction of video coding, the MSSC model is a theoretical abstraction of scalable video coding, which is an important application of network communications. We give an achievable region for the MSSC system. The given achievable region is tight when $Y$ is required to be reconstructed perfectly in the usual Shannon sense at the second stage. We also study the minimum total rate MSSC problem, and derive the minimum total rate for Gaussian sources. This result disproves the possibility that the minimum total rate of one stage sequential coding can be achieved at both stages even for correlated Gaussian sources. Thus we offer a theoretical explanation for the performance loss of scalable video coding widely noted by practitioners.