Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms

Jan Ostergaard, Yuval Kochman, Ram Zamir

Research output: Contribution to journalArticlepeer-review


It is well known that Shannon's rate-distortion function (RDF) in the colored quadratic Gaussian (QG) case can be parametrized via a single Lagrangian variable (the water level in the reverse water filling solution). In this paper, we show that the symmetric colored QG multiple description (MD) RDF in the case of two descriptions can be parametrized in the spectral domain via two Lagrangian variables, which control the tradeoff between the side distortion, the central distortion, and the coding rate. This spectral-domain analysis is complemented by a time-domain scheme-design approach: we show that the symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma modulation and differential pulse-code modulation. In particular, two source prediction loops, one for each description, are embedded within a common noise-shaping loop, whose parameters are explicitly found from the spectral-domain characterization.

Original languageEnglish
Article number7369969
Pages (from-to)5465-5483
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2016


  • KKT optimality conditions
  • Multiple-description coding
  • delta-sigma quantization
  • noise shaping
  • optimization
  • predictive coding
  • rate-distortion theory

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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