Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints

Photios A. Stavrou, Jan Østergaard*, Mikael Skoglund

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)
19 Downloads (Pure)

Abstract

In this paper, we derive lower and upper bounds on the OPTA of a two-user multi-input multi-output (MIMO) causal encoding and causal decoding problem. Each user's source model is described by a multidimensional Markov source driven by additive i.i.d. noise process subject to three classes of spatio-temporal distortion constraints. To characterize the lower bounds, we use state augmentation techniques and a data processing theorem, which recovers a variant of rate distortion function as an information measure known in the literature as nonanticipatory e-entropy, sequential or nonanticipative RDF. We derive lower bound characterizations for a system driven by an i.i.d. Gaussian noise process, which we solve using the SDP algorithm for all three classes of distortion constraints. We obtain closed form solutions when the system's noise is possibly non-Gaussian for both users and when only one of the users is described by a source model driven by a Gaussian noise process. To obtain the upper bounds, we use the best linear forward test channel realization that corresponds to the optimal test channel realization when the system is driven by a Gaussian noise process and apply a sequential causal DPCM-based scheme with a feedback loop followed by a scaled ECDQ scheme that leads to upper bounds with certain performance guarantees. Then, we use the linear forward test channel as a benchmark to obtain upper bounds on the OPTA, when the system is driven by an additive i.i.d. non-Gaussian noise process. We support our framework with various simulation studies.

Original languageEnglish
Article number842
JournalEntropy
Volume22
Issue number8
Number of pages32
ISSN1099-4300
DOIs
Publication statusPublished - 30 Jul 2020

Keywords

  • Bounds
  • Causal coding
  • Convex programming
  • Estimation
  • Multi-user rate distortion theory
  • One-shot information theory
  • Spatial distortion constraints
  • Temporal distortion constraints

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