On the sum-rate loss of quadratic Gaussian multiterminal source coding

Yang Yang, Yifu Zhang, Zixiang Xiong

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Abstract

This work studies the sum-rate loss of quadratic Gaussian multiterminal source coding, i.e., the difference between the minimum sum-rates of distributed encoding and joint encoding (both with joint decoding) of correlated Gaussian sources subject to MSE distortion constraints on individual sources. It is shown that under the non-degraded assumption, i.e., all target distortions are simultaneously achievable by a Berger-Tung scheme, the supremum of the sum-rate loss of distributed encoding over joint encoding of L jointly Gaussian sources increases almost linearly in the number of sources L, with an asymptotic slope of 0.1083 b/s per source as L goes to infinity. This result is obtained even though we currently do not have the full knowledge of the minimum sum-rate for the distributed encoding case. The main idea is to upper-bound the minimum sum-rate of multiterminal source coding by that achieved by parallel Gaussian test channels while lower-bounding the minimum sum-rate of joint encoding by a reverse water-filling solution to a relaxed joint encoding problem of the same set of Gaussian sources with a sum-distortion constraint (that equals the sum of the individual target distortions). We show that under the non-degraded assumption, the supremum difference between the upper bound for distributed encoding and the lower bound for joint encoding is achieved in the bi-eigen equal-variance with equal distortion case, in which both bounds are known to be tight.

Original languageEnglish
Title of host publicationProceedings of 2010 IEEE International Symposium on Information Theory (ISIT 2010)
Subtitle of host publication13-18 June 2010, Austin, TX, USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages41-45
Number of pages5
ISBN (Print)9781424469604
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventIEEE International Symposium on Information Theory 2010 - Austin, United States of America
Duration: 13 Jun 201018 Jun 2010
https://ieeexplore.ieee.org/xpl/conhome/5508195/proceeding (Proceedings)

Conference

ConferenceIEEE International Symposium on Information Theory 2010
Abbreviated titleISIT 2010
CountryUnited States of America
CityAustin
Period13/06/1018/06/10
Internet address

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