Matched Multiuser Gaussian Source Channel Communications via Uncoded Schemes

We investigate whether uncoded schemes are optimal for Gaussian sources on multiuser Gaussian channels. Particularly, we consider two problems: the first is to send correlated Gaussian sources on a Gaussian broadcast channel where each receiver is interested in reconstructing only one source compone...

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Veröffentlicht in:IEEE transactions on information theory Jg. 63; H. 7; S. 4155 - 4171
Hauptverfasser: Chao Tian, Jun Chen, Diggavi, Suhas N., Shitz, Shlomo Shamai
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.07.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Broadcast
combined source-channel coding
Decoding
Distortion
Distortion measurement
Encoding
Error analysis
Linear functions
multiple access
Noise measurement
Optimization
Receivers
ISSN:0018-9448, 1557-9654
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Zusammenfassung:We investigate whether uncoded schemes are optimal for Gaussian sources on multiuser Gaussian channels. Particularly, we consider two problems: the first is to send correlated Gaussian sources on a Gaussian broadcast channel where each receiver is interested in reconstructing only one source component (or one specific linear function of the sources) under the mean squared error distortion measure; the second is to send correlated Gaussian sources on a Gaussian multiple-access channel, where each transmitter observes a noisy combination of the sources, and the receiver wishes to reconstruct the individual source components (or individual linear functions) under the mean squared error distortion measure. It is shown that when the channel parameters satisfy certain general conditions, the induced distortion tuples are on the boundary of the achievable distortion region, and thus optimal. Instead of following the conventional approach of attempting to characterize the achievable distortion region, we ask the question whether and how a match can be effectively determined. This decision problem formulation helps to circumvent the difficult optimization problem often embedded in region characterization problems, and it also leads us to focus on the critical conditions in the outer bounds that make the inequalities become equalities, which effectively decouple the overall problem into several simpler sub-problems. Optimality results previously unknown in the literature are obtained using this novel approach. Explicit and novel outer bounds are derived for the two problems as the byproducts of our investigation.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2701807