(Almost) Practical Tree Codes

TL;DR

This paper advances the practicality of tree codes for networked control by demonstrating efficient sequential decoding algorithms for linear time-invariant tree codes, supported by simulations in control systems.

Contribution

It shows that linear time-invariant tree codes can be efficiently decoded with sequential algorithms, improving their practical applicability in control over noisy channels.

Findings

Sequential decoding achieves efficient decoding of LTI tree codes.

Numerical simulations confirm decoder effectiveness in control systems.

Trade-offs between performance loss and decoding complexity are characterized.

Abstract

We consider the problem of stabilizing an unstable plant driven by bounded noise over a digital noisy communication link, a scenario at the heart of networked control. To stabilize such a plant, one needs real-time encoding and decoding with an error probability profile that decays exponentially with the decoding delay. The works of Schulman and Sahai over the past two decades have developed the notions of tree codes and anytime capacity, and provided the theoretical framework for studying such problems. Nonetheless, there has been little practical progress in this area due to the absence of explicit constructions of tree codes with efficient encoding and decoding algorithms. Recently, linear time-invariant tree codes were proposed to achieve the desired result under maximum-likelihood decoding. In this work, we take one more step towards practicality, by showing that these codes can be efficiently decoded using sequential decoding algorithms, up to some loss in performance (and with some practical complexity caveats). We supplement our theoretical results with numerical simulations that demonstrate the effectiveness of the decoder in a control system setting.