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Prog. Theor. Phys. Supplement No.157 (2005) pp. 197-204
Statistical Mechanics of Source Coding with a Fidelity Criterion
Yoshiyuki Kabashima and
Tadaaki Hosaka
Department of Computational Intelligence and Systems Science,
Tokyo Institute of Technology, Yokohama 226-8502, Japan
Abstract:
We provide a method to evaluate the typical performance
of lossy data compression schemes for
general (discrete or continuous) memoryless sources
using the replica method (RM).
The proposed method reproduces a known
formula to compute the rate-distortion function
representing the optimal tradeoff
in the limit of infinite data lengths between
the compression rate and permissible distortion level,
which is consistent with existing methods
in information theory literature.
The advantage of the RM-based method
is the ability to accurately assess the performance of sub-optimal
code ensembles, demonstrated here for
Gaussian memoryless sources.
The obtained result is used to construct a family of
error correcting codes that are
composed of practical-size codebooks
and asymptotically achieve the capacity
of the Gaussian channel.
URL :
http://ptp.ipap.jp/link?PTPS/157/197/
DOI : 10.1143/PTPS.157.197
References:
- C. E. Shannon, IRE Nat. Conv. Rec. part 4 (1959), 142.
- I. Csiszár, IEEE Trans. Inform. Theory IT-20 (1974), 122.
- C. E. Shannon, Bell Syst. Tech. J. 27 (1948), 379; ibid. 27 (1948), 623.
-
D. J. Gross and M. Mézard, Nucl. Phys. B 240 (1984), 431[CrossRef].
-
T. Muratama and M. Okada, J. of Phys. A 36 (2003), 11123[IoP STACKS].
- S. Arimoto, IEEE Trans. Inform. Theory IT-18 (1972), 14.
- R. Blahut, IEEE Trans. Inform. Theory IT-18 (1972), 460.
- T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley & Sons, Inc., 1991).
-
J. R. L. de Almeida and D. J. Thouless, J. of Phys. A 11 (1977), 983[CrossRef].
- H. Nishimori, Prog. Theor. Phys. 66 (1981), 1169[PTP].
- T. Hosaka and Y. Kabashima, in Proceedings of International Symposium on Information Theory 2004 (2004), p. 479.
-
T. Hosaka and Y. Kabashima, cond-mat/0311123[e-print arXiv];
J. Phys. Soc. Jpn. 74 (2005), 488[JPSJ].
