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Tracking an Auto-Regressive Process with Limited Communication per Unit Time.

Rooji Jinan1, Parimal Parag2, Himanshu Tyagi2

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For high-dimensional processes, a "fast but loose" communication strategy is optimal with ideal codes. However, practical errors favor slower, more refined updates for better real-time estimation.

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Area of Science:

  • Information Theory
  • Signal Processing
  • Control Systems

Background:

  • Real-time estimation of high-dimensional time series is crucial in various fields.
  • Limited communication bandwidth necessitates efficient data transmission strategies.
  • Successive update schemes aim to balance estimation accuracy and communication delay.

Purpose of the Study:

  • To compare the optimality of "fast but loose" versus delayed refinement strategies for real-time estimation under bandwidth constraints.
  • To analyze the impact of quantization errors on the performance of successive update schemes.
  • To determine the optimal update frequency for practical scenarios.

Main Methods:

  • Analysis of a high-dimensional first-order auto-regressive process.
  • Modeling of a time-slotted communication system in a slow-sampling regime.
  • Mathematical derivation of optimality conditions for different update strategies.
  • Investigation of the effects of additive bias from quantization codes.

Main Results:

  • The "fast but loose" successive update scheme is asymptotically optimal for large dimensions with ideal spherical codes.
  • Practical quantization codes introduce bias, diminishing the optimality of the "fast but loose" approach.
  • A judiciously chosen update frequency, balancing speed and refinement, outperforms the "fast but loose" scheme in the presence of errors.

Conclusions:

  • The theoretical optimality of "fast but loose" communication does not always translate to practical applications due to real-world coding imperfections.
  • For systems with non-ideal quantization, a carefully selected update frequency is essential for optimal real-time estimation.
  • Future research should focus on developing robust coding and update strategies for practical high-dimensional estimation problems.