Lattices for Distributed Source Coding: Jointly Gaussian Sources and Reconstruction of a Linear Function

  • Dinesh Krithivasan
  • S. Sandeep Pradhan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


Consider a pair of correlated Gaussian sources (X 1,X 2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear combination of X 1 and X 2 to within a mean-square distortion of D. We obtain an inner bound to the optimal rate-distortion region for this problem. A portion of this inner bound is achieved by a scheme that reconstructs the linear function directly rather than reconstructing the individual components X 1 and X 2 first. This results in a better rate region for certain parameter values. Our coding scheme relies on lattice coding techniques in contrast to more prevalent random coding arguments used to demonstrate achievable rate regions in information theory. We then consider the case of linear reconstruction of K sources and provide an inner bound to the optimal rate-distortion region. Some parts of the inner bound are achieved using the following coding structure: lattice vector quantization followed by “correlated” lattice-structured binning.


Random Vector Rate Region Linear Code Gaussian Source Lattice Code 
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  1. 1.
    Gelfand, S., Pinsker, M.: Coding of Sources on the Basis of Observations with Incomplete Information. Problemy Peredachi Informatsii 15, 45–57 (1979)MathSciNetGoogle Scholar
  2. 2.
    Korner, J., Marton, K.: How to Encode the Modulo-Two Sum of Binary Sources. IEEE Trans. Inform. Theory 25, 219–221 (1979)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Csiszár, I., Korner, J.: Information Theory: Coding Theorems for Discrete Memoryless Systems. Academic Press, London (1981)zbMATHGoogle Scholar
  4. 4.
    Han, T.S., Kobayashi, K.: A Dichotomy of Functions F(X,Y) of Correlated Sources (X,Y). IEEE Trans. on Inform. Theory 33, 69–76 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ahlswede, R., Han, T.S: On Source Coding with Side Information via a Multiple-Access Channel and Related Problems in Multi-User Information Theory. IEEE Trans. on Inform. Theory 29, 396–412 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Berger, T.: Multiterminal Source Coding. Lectures presented at CISM summer school on the Inform. Theory approach to communications (1977)Google Scholar
  7. 7.
    Tung, S.-Y.: Multiterminal Source Coding. PhD thesis. Cornell University, Ithaca, NY (1978)Google Scholar
  8. 8.
    Wagner, A.B., Tavildar, S., Viswanath, P.: The Rate-Region of the Quadratic Gussian Two-Terminal Source-Coding Problem. arXiv:cs.IT/0510095Google Scholar
  9. 9.
    Zamir, R., Feder, M.: On Lattice Quantization Noise. IEEE Trans. Inform. Theory 42, 1152–1159 (1996)zbMATHCrossRefGoogle Scholar
  10. 10.
    Zamir, R., Shamai, S., Erez, U.: Nested Linear/Lattice Codes for Structured Multiterminal Binning. IEEE Trans. Inform. Theory 48, 1250–1276 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Erez, U., Zamir, R.: Achieving 1/2 log(1+SNR) on the AWGN Channel with Lattice Encoding and Decoding. IEEE Trans. Inform. Theory 50, 2293–2314 (2004)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Erez, U., Litsyn, S., Zamir, R.: Lattices Which Are Good for (Almost) Everything. IEEE Trans. Inform. Theory 51(10), 3401–3416 (2005)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Poltyrev, G.: On Coding Without Restrictions for the AWGN Channel. IEEE Trans. Inform. Theory 40, 409–417 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Krithivasan, D., Pradhan, S.S.: A Proof of the Existence of Good Nested Lattices,
  15. 15.
    Loeliger, H.A.: Averaging Bounds for Lattices and Linear Codes. IEEE Trans. Inform. Theory 43, 1767–1773 (1997)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dinesh Krithivasan
    • 1
  • S. Sandeep Pradhan
    • 1
  1. 1.Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109USA

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