Multiple Description Coding for Closed Loop Systems over Erasure Channels

In this paper, we consider robust source coding in closed-loop systems. In particular, we consider a (possibly) unstable LTI system, which is to be stabilized via a network. The network has random delays and erasures on the data-rate limited (digital) forward channel between the encoder (controller) and the decoder (plant). The feedback channel from the decoder to the encoder is assumed noiseless. Since the forward channel is digital, we need to employ quantization. We combine two techniques to enhance the reliability of the system. First, in order to guarantee that the system remains stable during packet dropouts and delays, we transmit quantized control vectors containing current control values for the decoder as well as future predicted control values. Second, we utilize multiple description coding based on forward error correction codes to further aid in the robustness towards packet erasures. In particular, we transmit M redundant packets, which are constructed such that when receiving any J packets, the current control signal as well as J-1 future control signals can be reliably reconstructed at the decoder. We prove stability subject to quantization constraints, random dropouts, and delays by showing that the system can be cast as a Markov jump linear system.