Error-Correcting Codes for Automatic Control

In many control-theory applications one can classify all possible states of the device by an infinite state graph with polynomially-growing expansion. In order for a controller to control or estimate the state of such a device, it must receive reliable communications from its sensors; if there is channel noise, the encoding task is subject to a stringent real-time constraint. We show a constructive on-line error correcting code that works for this class of applications. Our code is computationally efficient and enables on-line estimation and control in the presence of channel noise. It establishes a constructive (and optimal-within-constants) analog, for control applications, of the Shannon coding theorem.

Authors

• Rafail Ostrovsky
• Yuval Rabani
• Leonard J. Schulman

Keywords

• Error correction codes
• Automatic control
• Communication system control
• Base stations
• Application software
• Computer science
• Mathematics
• Polynomials
• Engines
• Space exploration
• Forward Error Correction
• Random Noise
• Control Applications
• State Of The Device
• Static Graph
• Parameter Space
• Finite Set
• Error Probability
• Base Station
• Dynamic Programming
• Exhaustive Search
• Time Segments
• Hamming Distance
• Codeword
• Quintuple
• Trajectory Length
• Code Length
• Efficient Construction
• Noisy Channels
• Code Blocks
• Convolutional Codes
• Code Construction
• Grid Graph