# Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-offs

arXiv: https://arxiv.org/abs/1411.7632 · HTML: https://mlsanity.com/paper/1411.7632/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2014.

## Built on by (most cited first, 4 of 4)

- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Sub-optimality of the Separation Principle for Quadratic Control from Bilinear Observations](https://mlsanity.com/paper/2504.11555/) (2025)
- [Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation](https://mlsanity.com/paper/2606.00703/) (2026)
- [Reinforcement Learning for Jointly Optimal Coding and Control Policies for a Controlled Markovian System over a Communication Channel](https://mlsanity.com/paper/2411.13884/) (2024)

## Abstract (arXiv)

Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimator's performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed.