Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1609.01383

Rate-Distortion Analysis of Quantizers with Error Feedback

Shuichi Ohno·Teruyuki Shiraki·M. Rizwan Tariq·Masaaki Nagahara
View original source ↗Read source document ↗Export metadata ↓

Abstract

A Delta-Sigma modulator that is often utilized to convert analog signals into digital signals can be modeled as a static uniform quantizer with an error feedback filter. In this paper, we present a rate-distortion analysis of quantizers with error feedback including the Delta-Sigma modulators, assuming that the error owing to overloading in the static quantizer is negligible. We demonstrate that the amplitude response of the optimal error feedback filter that minimizes the mean squared quantization error can be parameterized by one parameter. This parameterization enables us to determine the optimal error feedback filter numerically. The relationship between the number of bits used for the quantization and the achievable mean squared error can be obtained using the optimal error feedback filter. This clarifies the rate-distortion property of quantizers with error feedback. Then, ideal optimal error feedback filters are approximated by practical filters using the Yule-Walker method and the linear matrix inequality-based method. Numerical examples are provided for demonstrating our analysis and synthesis.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shuichi Ohno, Teruyuki Shiraki, M. Rizwan Tariq, Masaaki Nagahara. 2016-09-06. Rate-Distortion Analysis of Quantizers with Error Feedback. https://doi.org/10.1109/tsp.2017.2745450

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Ensuring Stability of Non-Minimal Modes in Input-Output Data-Driven Representation

Many recent data-driven control approaches for linear time-invariant systems are based on output trajectory prediction using input-output data matrices. The system dynamics described by this predictor, which we refer to as the input-output data-driven representation, yields non-unique autoregressive with exogenous inputs (ARX) models having possibly unstable non-minimal modes. In this note, we show that the stability of these non-minimal modes is ensured by a certain choice of ARX model, which coincides with the minimum-norm least-squares predictor using the Moore-Penrose inverse of the data matrix. This stability guarantee holds regardless of the underlying system's stability. Moreover, the stability persists under sufficiently small noise in data when a suitably truncated Moore-Penrose inverse is used. Consequently, the ARX model need not be reduced to the true system order in order to avoid unstable additional modes.

eess.SY↗
arXiv2026

Optimization-Based Formation Flight on Libration Point Orbits

A model predictive control (MPC) framework is developed for station-keeping in spacecraft formation flight along libration point orbits. At each control period, the MPC policy solves a multi-vehicle optimal control problem (MVOCP) that tracks a reference trajectory, while enforcing path constraints on the relative motion of the formation. The control policy makes use of a limited set of control nodes consistent with operational constraints that allow only a small number of maneuver opportunities per revolution. To promote recursive feasibility, path constraints are progressively tightened across the prediction horizon. An isoperimetric reformulation of the constraints is used to prevent inter-sample violations. The resulting MVOCP is a nonconvex program, which is solved via sequential convex programming. The proposed approach is evaluated in a high-fidelity ephemeris model under uncertainties for a formation along the near-rectilinear halo orbit (NRHO), and subject to path constraints on inter-spacecraft separation and relative Sun phase angle. The results demonstrate maintenance of a spacecraft formation that satisfies the path constraints with realistic cumulative propellant consumption.

eess.SY↗
arXiv2026

Certificates Synthesis for A Class of Observational Properties in Stochastic Systems: A Unified Approach

In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of observational properties, which characterize the inferences an external observer can draw from system outputs. These properties are formulated as probabilistic hyperproperties based on HyperLTL over finite traces, yielding a unified framework that subsumes several existing notions studied separately in the literature. We reduce the verification problem to reachability analysis over an augmented structure that integrates the system dynamics with an automaton representation of the specification. Building on this construction, we develop stochastic barrier certificates that provide probabilistic guarantees for property satisfaction while avoiding explicit state-space discretization. The effectiveness of the proposed framework is demonstrated through a case study.

eess.SY↗