Skip to main content
SpringerLink
Log in

Successively Structured Gaussian Two-terminal Source Coding

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Multiterminal source coding refers to separate encoding and joint decoding of multiple correlated sources. Joint decoding requires all the messages to be decoded simultaneously which is exponentially more complex than a sequence of single-message decodings. Inspired by previous work on successive coding, we apply the successive Wyner-Ziv coding, which is inherently a low complexity approach of obtaining a prescribed distortion, to the two-terminal source coding scheme. First, we consider 1-helper problem where one source provides partial side information to the decoder to help the reconstruction of the main source. Our results show that the successive coding strategy is an optimal strategy in the sense of achieving the rate-distortion function. By developing connections between source encoding and data fusion steps, it is shown that the whole rate-distortion region for the 2-terminal source coding problem is achievable using the successive coding strategy. Comparing the performance of the sequential coding with the performance of the successive coding, we show that there is no sum-rate loss when the side information is not available at the encoder. This result is of special interest in some applications such as video coding where there are processing and storage constraints at the encoder. Finally, we provide an achievable rate-distortion region for the m-terminal source coding.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gelfand S.I., Pinsker M.S. (1979) Coding of sources on the basis of observations with incomplete information. Problems of Information Transmission 15(2): 115–125

    MathSciNet  Google Scholar 

  2. Yamamoto H., Itoh K. (1980) Source coding theory for multiterminal communication systems with a remote source. Transactions of IECE Japan, E 63(10): 700–706

    Google Scholar 

  3. Flynn T.J., Gray R.M. (1987) Encoding of correlated observations. IEEE Transactions on Information Theory 33(6): 773–787

    Article  MathSciNet  Google Scholar 

  4. Berger T., Zhang Z., Viswanathan H. (1996) The CEO problem. IEEE Transactions on Information Theory 42(3): 887–902

    Article  MATH  MathSciNet  Google Scholar 

  5. Berger, T. (1978). Multiterminal source coding. In G. Longo (Ed.). The Information Theory Approach to Communications (CISM Courses and Lectures, no. 229) (pp. 171–231). Vienna, Austria: Springer-Verlag.

  6. Wagner A.B., Tavildar S., Viswanath P. (2008) The rate region of the Quadratic Gaussian two-terminal source-coding problem. IEEE Transactions on Information Theory 54(5): 1938–1961

    Article  MathSciNet  Google Scholar 

  7. Servetto, S. D. The sum-rate of multiterminal source coding with two encoders. IEEE Transactions on Information Theory, submitted for publication, Apr. 2006 (original title: The Region of Achievable Rates for Multiterminal Source Coding, Part I).

  8. Draper, S. C. (2002). Successive structuring of source coding algorithms for data fusion, buffering, and distribution in networks, Ph.D. dissertation, Cambridge, MA: Massachusetts Institute of Technology (MIT), Jun. 2002.

  9. Natrio, L., Brites, C., Ascenso, J., & Pereira, F. (2005). Extrapolating side information for low-delay pixel-domain distributed video coding. Int. Workshop on Very Low Bitrate Video Coding, Sardinia, Italy, Sept. 2005.

  10. Shamai S., Verdu S., Zamir R. (1998) Systematic lossy source/channel coding. IEEE Transactions on Information Theory 44(2): 564–579

    Article  MATH  MathSciNet  Google Scholar 

  11. Girod, B., Aaron, A., Rane, S., & Rebollo-Monedero, D. (2005). Distributed video coding. Proceedings of the IEEE, 93(1), 71–83, Jan. 2005. Invited paper, Special Issue on Video Coding and Delivery.

  12. Wyner A.D., Ziv J. (1976) The rate-distortion function for source coding with side information at the decoder. IEEE Transactions on Information Theory 22(1): 1–10

    Article  MATH  MathSciNet  Google Scholar 

  13. Wyner A.D. (1978) The rate-distortion function for source coding with side information at the decoder II: General sources. Information and Control 38(1): 60–80

    Article  MATH  MathSciNet  Google Scholar 

  14. Xiong, Z., Stankovic, V., Cheng, S., Liveris, A., & Sun, Y. (2004). Source-channel coding for algebraic multiterminal binning. In Proceedings on IEEE Information Theory Workshop (ITW), San Antonio, Texas, Oct. 2004.

  15. Costa M. (1983) Writing on Dirty Paper. IEEE Transactions on Information Theory 29(3): 439–441

    Article  MATH  Google Scholar 

  16. Eswaran, K. (2006). Remote source coding and AWGN CEO problems. Master’s thesis, EECS Department, University of California, Berkeley, Jan. 2006.

  17. Oohama Y. (1997) Gaussian multiterminal source coding. IEEE Transactions on Information Theory 43(6): 1912–1923

    Article  MATH  MathSciNet  Google Scholar 

  18. Pandya, A., Kansal, A., Pottie, G. J., & Srivastava, M. B. (2004). Lossy source coding of multiple Gaussian sources: m-helper problem. In Proceedings on IEEE Information Theory Workshop (ITW), San Antonio, Texas, Oct. 2004.

  19. Oohama, Y. (1999). Multiterminal source coding for correlated memoryless Gaussian sources with several side information at the decoder. In Proceedings on IEEE Information Theory Workshop, p. 100, Kruger National Park, South Africa, Jun. 1999.

  20. Oohama Y. (2005) Rate-distortion theory for Gaussian multiterminal source coding systems with several side informations at the decoder. IEEE Transactions on Information Theory 51(7): 2577–2593

    Article  MathSciNet  Google Scholar 

  21. Oohama, Y. (2006). Gaussian multiterminal source coding with several side informations at the decoder. In Proceedings on IEEE Int. Symp. Information Theory (ISIT), Seattle, Washington, Jul. 2006.

  22. Berger T., Yeung R. (1989) Multiterminal source encoding with one distortion criterion. IEEE Transactions on Information Theory 35(2): 228–236

    Article  MATH  MathSciNet  Google Scholar 

  23. Tung, S. Y. (1978). Multiterminal source coding. Ph.D. Thesis, School of Electrical Engineering, Cornell University, Ithaca, NY, May 1978.

  24. Oohama, Y. (2006). Separate source coding of correlated Gaussian remote sources. In Proceedings on 2006 Information Theory and Applications Workshop, San Diego, CA, USA, Jan. 2006.

  25. Koshelev V.N. (1980) Hierarchical coding of discrete sources. Problemy Peredachi Informatsti 16(3): 31–49

    MathSciNet  Google Scholar 

  26. Equitz W.H.R., Cover T.M. (1991) Successive refinement of information. IEEE Transactions on Information Theory 37(2): 269–275

    Article  MATH  MathSciNet  Google Scholar 

  27. Rimoldi B. (1994) Successive refinement of information: Characterization of achievable rates. IEEE Transactions on Information Theory 40(1): 253–259

    Article  MATH  MathSciNet  Google Scholar 

  28. Steinberg Y., Merhav N. (2004) On successive refinement for the Wyner-Ziv problem. IEEE Transactions on Information Theory 50(8): 1636–1654

    Article  MathSciNet  Google Scholar 

  29. Cheng S., Xiong Z. (2005) Successive refinement for the Wyner-Ziv problem and layered code design. IEEE Transactions on Signal Processing 53(8): 3269–3281

    Article  MathSciNet  Google Scholar 

  30. Tian C., Diggavi S. (2007) On multistage successive refinement for Wyner-Ziv source coding with degraded side information. IEEE Transactions on Information Theory 53(8): 2946–2960

    Article  MathSciNet  Google Scholar 

  31. Viswanathan H., Berger T. (1997) The Quadratic Gaussian CEO problem. IEEE Transactions on Information Theory 43(5): 1549–1559

    Article  MATH  MathSciNet  Google Scholar 

  32. Chen J., Zhang X., Berger T., Wicker S.B. (2004) An upper bound on the sum-rate distortion function and its corresponding rate allocation schemes for the CEO problem. IEEE Journal on Selected Areas in Communications 22(6): 977–987

    Article  Google Scholar 

  33. Prabhakaran, V., Tse, D., & Ramchandran, K. (2004). Rate region of the Quadratic Gaussian CEO problem. In Proc. IEEE Int. Symp. Information Theory (ISIT), June 2004, p. 119.

  34. Chen J., Berger T. (2008) Successive Wyner-Ziv coding scheme and its application to the Quadratic Gaussian CEO problem. IEEE Transactions on Information Theory 54(4): 1586–1603

    Article  MathSciNet  Google Scholar 

  35. Behroozi H., Soleymani M.R. (2007) Distortion sum-rate performance of successive coding strategy in quadratic Gaussian CEO problem. IEEE Transactions on Wireless Communications 6(12): 4361–4365

    Article  Google Scholar 

  36. Behroozi, H., & Soleymani, M. R. (2006). Successively structured Gaussian CEO problem. In Proceedings on IEEE Global Telecommunications Conference (GLOBECOM 2006), San Francisco, CA, Nov. 2006.

  37. Viswanathan H., Berger T. (2000) Sequential coding of correlated sources. IEEE Transactions on Information Theory 46(1): 236–246

    Article  MATH  MathSciNet  Google Scholar 

  38. Barron R.J., Chen B., Wornell G.W. (2003) The duality between information embedding and source coding with side information and some applications. IEEE Transactions on Information Theory 49(5): 1159–1180

    Article  MATH  MathSciNet  Google Scholar 

  39. Pradhan S.S., Chou J., Ramchandran K. (2003) Duality between source coding and channel coding and its extension to the side information case. IEEE Transactions on Information Theory 49(5): 1181–1203

    Article  MATH  MathSciNet  Google Scholar 

  40. Cover T.M., Thomas J.A. (1991) Elements of information theory. Wiley, New York

    MATH  Google Scholar 

  41. Yang, Y., Stankovic, V., Xiong, Z., & Zhao, W. (2005). On multiterminal source code design. In Proceedings on IEEE Data Compression Conference (DCC), Snowbird, Utah, Mar. 2005.

  42. Yang Y., Stankovic V., Xiong Z., Zhao W. (2008) On multiterminal source code design. IEEE Transactions on Information Theory 54(5): 2278–2302

    Article  MathSciNet  Google Scholar 

  43. Ma, N., Wang, Y., & Ishwar, P. (2007). Delayed sequential coding of correlated sources. 2nd Int. Workshop on Information Theory and its Applications, San Diego, CA, USA, Jan. 2007.

  44. Papoulis, A. (1991). Probability, random variables, and stochastic processes. McGraw- Hill.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, ON, Canada, K7L 3N6

    Hamid Behroozi

  2. Electrical and Computer Engineering Department, Concordia University, Montreal, QC, Canada, H3G 1M8

    M. Reza Soleymani

Authors
  1. Hamid Behroozi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Reza Soleymani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamid Behroozi.

Additional information

This paper was presented in part at the IEEE International Symposium on Information Theory (ISIT), July 2006 and in part at the IEEE Vehicular Technology Conference (VTC), September 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Behroozi, H., Reza Soleymani, M. Successively Structured Gaussian Two-terminal Source Coding. Wireless Pers Commun 48, 485–510 (2009). https://doi.org/10.1007/s11277-008-9534-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-008-9534-x

Keywords

Search

Navigation