Robust pedictive quantization: Analysis and design via convex optimization

Alyson K. Fletcher, Sundeep Rangan, Vivek K. Goyal, Kannan Ramchandran

Research output: Contribution to journalArticle

Abstract

Predictive quantization is a simple and effective method for encoding slowly-varying signals that is widely used in speech and audio coding. It has been known qualitatively that leaving correlation in the encoded samples can lead to improved estimation at the decoder when encoded samples are subject to erasure. However, performance estimation in this case has required Monte Carlo simulation. Provided here is a novel method for efficiently computing the mean-squared error performance of a predictive quantization system with erasures via a convex optimization with linear matrix inequality constraints. The method is based on jump linear system modeling and applies to any autoregressive moving average (ARMA) signal source and any erasure channel described by an aperiodic and irreducible Markov chain. In addition to this quantification for a given encoder filter, a method is presented to design the encoder filter to minimize the reconstruction error. Optimization of the encoder filter is a nonconvex problem, but we are able to parameterize with a single scalar a set of encoder filters that yield low MSE. The design method reduces the prediction gain in the filter, leaving the redundancy in the signal for robustness. This illuminates the basic tradeoff between compression and robustness.

Original languageEnglish (US)
Pages (from-to)618-632
Number of pages15
JournalIEEE Journal on Selected Topics in Signal Processing
Volume1
Issue number4
DOIs
StatePublished - Dec 2007

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Convex optimization
Linear matrix inequalities
Markov processes
Redundancy
Linear systems
Monte Carlo simulation

Keywords

  • Differential pulse code modulation
  • Erasure channels
  • Joint source-channel coding
  • Linear matrix inequalities

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

Robust pedictive quantization : Analysis and design via convex optimization. / Fletcher, Alyson K.; Rangan, Sundeep; Goyal, Vivek K.; Ramchandran, Kannan.

In: IEEE Journal on Selected Topics in Signal Processing, Vol. 1, No. 4, 12.2007, p. 618-632.

Research output: Contribution to journalArticle

Fletcher, Alyson K. ; Rangan, Sundeep ; Goyal, Vivek K. ; Ramchandran, Kannan. / Robust pedictive quantization : Analysis and design via convex optimization. In: IEEE Journal on Selected Topics in Signal Processing. 2007 ; Vol. 1, No. 4. pp. 618-632.
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