Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate

Yang Yang; Zixiang Xiong

doi:10.1109/ISIT.2011.6034077

Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate

Yang Yang
, Zixiang Xiong

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other › peer-review

6 Citations (Scopus)

Abstract

We consider the problem of distributed compression of the difference Z = Y₁ cY₂ of two jointly Gaussian sources Y₁ and Y₂ (with positive correlation coefficient ρ and positive c) under an MSE distortion constraint D on Z. The rate region for this problem is unknown. We provide a new lower bound on the minimum sum-rate by utilizing the connection of the above problem with the two-terminal source coding problem with matrix-distortion constraint. Our lower bound not only improves existing bounds in many cases, but also allows us to prove sum-rate tightness of the Berger-Tung scheme when c is either relatively small or large and D is larger than some threshold. Furthermore, our lower bound enables us to show that the improved lattice-based scheme recently introduced in [1] (with the smallest achievable sum-rate) performs within 1.18 b/s from the optimal sum-rate for all values of ρ, c, and D.

Original language	English
Title of host publication	2011 IEEE International Symposium on Information Theory Proceedings (ISIT 2011)
Subtitle of host publication	St. Petersburg, Russia, 31 July – 5 August 2011
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	2766-2770
Number of pages	5
ISBN (Print)	9781457705953, 9781457705960
DOIs	https://doi.org/10.1109/ISIT.2011.6034077
Publication status	Published - 2011
Externally published	Yes
Event	IEEE International Symposium on Information Theory 2011 - St. Petersburg, Russian Federation Duration: 31 Jul 2011 → 5 Aug 2011 https://ieeexplore.ieee.org/xpl/conhome/6026198/proceeding (Proceedings)

Conference

Conference	IEEE International Symposium on Information Theory 2011
Abbreviated title	ISIT 2011
Country/Territory	Russian Federation
City	St. Petersburg
Period	31/07/11 → 5/08/11
Internet address	https://ieeexplore.ieee.org/xpl/conhome/6026198/proceeding (Proceedings)

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10.1109/ISIT.2011.6034077

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Yang, Y., & Xiong, Z. (2011). Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate. In 2011 IEEE International Symposium on Information Theory Proceedings (ISIT 2011): St. Petersburg, Russia, 31 July – 5 August 2011 (pp. 2766-2770). Article 6034077 IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2011.6034077

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abstract = "We consider the problem of distributed compression of the difference Z = Y1 cY2 of two jointly Gaussian sources Y1 and Y2 (with positive correlation coefficient ρ and positive c) under an MSE distortion constraint D on Z. The rate region for this problem is unknown. We provide a new lower bound on the minimum sum-rate by utilizing the connection of the above problem with the two-terminal source coding problem with matrix-distortion constraint. Our lower bound not only improves existing bounds in many cases, but also allows us to prove sum-rate tightness of the Berger-Tung scheme when c is either relatively small or large and D is larger than some threshold. Furthermore, our lower bound enables us to show that the improved lattice-based scheme recently introduced in [1] (with the smallest achievable sum-rate) performs within 1.18 b/s from the optimal sum-rate for all values of ρ, c, and D.",

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Yang, Y & Xiong, Z 2011, Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate. in 2011 IEEE International Symposium on Information Theory Proceedings (ISIT 2011): St. Petersburg, Russia, 31 July – 5 August 2011., 6034077, IEEE, Institute of Electrical and Electronics Engineers, pp. 2766-2770, IEEE International Symposium on Information Theory 2011, St. Petersburg, Russian Federation, 31/07/11. https://doi.org/10.1109/ISIT.2011.6034077

Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate. / Yang, Yang; Xiong, Zixiang.
2011 IEEE International Symposium on Information Theory Proceedings (ISIT 2011): St. Petersburg, Russia, 31 July – 5 August 2011. IEEE, Institute of Electrical and Electronics Engineers, 2011. p. 2766-2770 6034077.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other › peer-review

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Distributed compression of linear functions: Partial sum-rate tightness and gap to optimal sum-rate

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