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On the Asymptotic Optimality of a Low-Complexity Coding Strategy for WSS, MA, and AR Vector Sources.

Jesús Gutiérrez-Gutiérrez¹, Marta Zárraga-Rodríguez¹, Xabier Insausti¹

¹Tecnun, University of Navarra, Paseo Manuel Lardizábal 13, 20018 San Sebastián, Spain.

Entropy (Basel, Switzerland)

|December 6, 2020

Summary

This study analyzes a coding strategy for Gaussian vector sources, focusing on its convergence speed for stationary, moving average, and autoregressive data. The research also examines performance with perturbed data, identifying conditions to maintain coding rate convergence speed.

Keywords:

autoregressive (AR) vector source low-complexity moving average (MA) vector source source coding wide sense stationary (WSS) vector source

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Area of Science:

Information Theory
Signal Processing
Data Compression

Background:

Efficiently encoding Gaussian vector sources is crucial for data compression and transmission.
Low-complexity coding strategies are desirable for practical applications.
Understanding asymptotic optimality and convergence rates is key to evaluating coding performance.

Purpose of the Study:

To investigate the asymptotic optimality of a specific low-complexity coding strategy for Gaussian vector sources.
To analyze the convergence speed of the coding rate for wide sense stationary (WSS), moving average (MA), and autoregressive (AR) vector sources.
To evaluate the coding strategy's performance on perturbed versions of these sources and identify conditions for preserved convergence speed.

Main Methods:

Asymptotic analysis of coding strategy performance.
Mathematical derivation of convergence rates for WSS, MA, and AR sources.
Perturbation analysis of source models to assess robustness.

Main Results:

The study establishes the asymptotic optimality of the low-complexity coding strategy.
Convergence speed analysis reveals performance characteristics for WSS, MA, and AR sources.
A sufficient condition is derived for perturbed sources, ensuring the convergence speed of the rate remains unchanged.

Conclusions:

The low-complexity coding strategy demonstrates strong performance for key Gaussian vector source types.
The strategy is robust to certain types of data perturbations, maintaining its efficiency.
This research contributes to the development of practical and efficient data compression techniques for complex data sources.