Source coding and channel requirements for unstable processes

Our understanding of information in systems has been based on the foundation of memoryless processes. Extensions to stable Markov and auto-regressive processes are classical. Berger proved a source coding theorem for the marginally unstable Wiener process, but the infinite-horizon exponentially unstable case has been open since Gray's 1970 paper. There were also no theorems showing what is needed to communicate such processes across noisy channels. In this work, we give a fixed-rate source-coding theorem for the infinite-horizon problem of coding an exponentially unstable Markov process. The encoding naturally results in two distinct bitstreams that have qualitatively different QoS requirements for communicating over a noisy medium. The first stream captures the information that is accumulating within the nonstationary process and requires sufficient anytime reliability from the channel used to communicate the process. The second stream captures the historical information that di...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Anant Sahai, Sanjoy K. Mitter
• Keywords: CORR 2006, Education, Unstable Case, Unstable Markov Process, Unstable Wiener Process