The random energy model in a magnetic field and joint source-channel coding

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 22, 2008, Pages 5662-5674

  Merhav, Neri ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Information theory; Joint source channel codes; Magnetization; Phase transitions; REM; Spin glasses

Indexed keywords

CODES (SYMBOLS); FERROMAGNETISM; IMAGE CODING; INFORMATION THEORY; MAGNETIC FIELD MEASUREMENT; MAGNETIC FIELDS; MAGNETIC MATERIALS; MAGNETIC PROPERTIES; MAGNETISM; PROGRAMMING THEORY; RANDOM PROCESSES;

(E ,2E) THEORY; (PL) PROPERTIES; (SKEW) FREE ENERGY; APPLIED (CO); CODING PROBLEMS; DERRIDA; ELSEVIER (CO); ENSEMBLE PERFORMANCE; EXTERNAL MAGNETIC FIELDS; JOINT SOURCE CHANNEL CODES (JSCC); JOINT SOURCE/CHANNEL CODING (JSCC); MAGNETIC (CE); NON UNIFORMITIES; RANDOM CODING; RANDOM ENERGY MODEL (REM); TYPICAL PATTERNS;

CHANNEL CODING;

EID: 47649121727     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2008.05.040     Document Type: Article

References (36)

1. Hosaka T., and Kabashima Y. Statistical mechanical approach to error exponents of lossy data compression. J. Phys. Soc. Japan 74 1 (2005) 488-497
2. Mutayama T. Statistical mechanics of the data compression theorem. J. Phys. A: Math. Gen. 35 (2002) L95-L100
3. Kabashima Y., and Hosaka T. Statistical mechanics for source coding with a fidelity criterion. Progr. Theor. Phys. Supplement no. 157 (2005) 197-204
4. K. Tadaki, A statistical mechanical interpretation of instantaneous codes, Proc. ISIT 2007, pp. 1906-1910, Nice, France, June 2007
5. M. Mézard, A. Montanari, Information, Physics and Computation, draft, November 9, 2007. Available on-line at http://www.stanford.edu/~montanar/BOOK/book.html
6. Kanter I., and Saad D. Error-correcting codes that nearly saturate Shannon's bound. Phys. Rev. Lett. 83 13 (1999) 2660-2663
7. Procacci A., and Scoppola B. Statistical mechanics approach to coding theory. J. Stat. Phys. 96 3/4 (1999) 907-912
8. Sourlas N. Spin-glass models as error-correcting codes. Nature 339 (1989) 693-695
9. Sourlas N. Spin glasses, error-correcting codes and finite-temperature decoding. Europhys. Lett. 25 (1994) 159-164
10. Kabashima Y., Sazuka N., Nakamura K., and Saad D. Tighter decoding reliability bound for Gallager's error-correcting code. Phys. Rev. E 64 (2001) 046113-1-046113-4
11. Kabashima Y., and Saad D. Statistical mechanics of error correcting codes. Europhysics Lett. 45 1 (1999) 97-103
12. O. Shental, I. Kanter, Shannon capacity of infinite-range spin-glasses, Technical report, Bar Ilan University, 2005
13. T. Mora, O. Rivoire, Statistical mechanics of error exponents for error-correcting codes, arXiv:cond-mat/0606696. June 2006
14. A. Montanari, Two lectures on iterative decoding and statistical mechanics, arXiv:cond-mat/0512296. December 14, 2005
15. S. Franz, M. Leone, A. Montanari, F. Ricci-Tersenghi, The dynamic phase transition for decoding algorithms, arXiv:cond-mat/020505, May 2, 2002
16. A. Montanari, R. Urbanke, Modern coding theory: The statistical mechanics and computer science point of view, preprint 2007
17. A. Montanari, The glassy phase of Gallager codes, arXiv:cond-mat/0104079v1 April 4, 2001
18. Ruján P. Finite temperature error-correcting codes. Phys. Rev. Lett. 70 19 (May 1993) 2968-2971
19. Montanari A. Tight bounds for LDPC and LDGM codes under MAP decoding. IEEE Trans. Inform. Theory 51 9 (2005) 3221-3246
20. Dorlas T.C., and Wedagedera J.R. Phase diagram of the random energy model with higher order ferromagnetic term and error correcting codes due to Sourlas. Phys. Rev. Lett. 83 21 (1999) 4441-4444
21. Saaskyan D.B. Solution of dilute Derrida model. Teo. Mat. Fiz. 97 (1993) 1199-1205
22. Saaskyan D.B. Finite-volume effects in the ferromagnetic phase of the Derrida model at absolute zero in connection with coding. JETP Lett. 61 8 (1995) 650-654
23. Allakhverdyan A.E., and Saaskyan D.B. Finite-volume corrections to the magnetization in the spin-glass phase of the Derrida model. Theoret. Math. Phys. 109 3 (1996) 1574-1577
24. Allakhverdyan A.E., and Saaskyan D.B. Finite-size effects for the dilute coupling Derrida model. Nucl. Phys. B 498 (1997) 604-618
25. Saaskian D.B. Error threshold in optimal coding, numerical criteria, and classes of universality for complexity. Phys. Rev.E 71 (2005) 016126
26. Derrida B. Random-energy model: Limit of a family of disordered models. Phys. Rev. Lett. 45 2 (1980) 79-82
27. Derrida B. The random energy model. Phys. Rep. 67 1 (1980) 29-35 (Review Section of Physics Letters)
28. Derrida B. Random-energy model: An exactly solvable model for disordered systems. Phys. Rev. B 24 5 (1981) 2613-2626
29. N. Merhav, Relations between random coding exponents and the statistical physics of random codes, submitted to IEEE Trans. Inform. Theory, (August 2007). Available on-line at: http://www.ee.technion.ac.il/people/merhav/papers/p117.pdf (submitted for publication)
30. Cover T.M., and Thomas J.A. Elements of Information Theory. second ed. (2006), John Wiley & Sons
31. Gallager R.G. Information Theory and Reliable Communication (1968), John Wiley & Sons
32. Mandl F. Statistical Physics (1971), John Wiley & Sons
33. Edwards S.F., and Anderson P.W. Theory of spin glasses. J. Phys. F 5 (1975) 965-974
34. Sherrington D., and Kirkpatrick S. Solvable model of a spin glass. Phys. Rev. Lett. 35 (1975) 1792-1796
35. Derrida B., and Gardner E. Solution of the generalised random energy model. J. Phys. C: Solid State Phys. 19 (1986) 2253-2274
36. N. Merhav, Error exponents of erasure/list decoding revisited via moments of distance enumerators, IEEE Trans. Inform. Theory, (November 2007). Also, available on-line at: http://www.ee.technion.ac.il/people/merhav/papers/p119.pdf (submitted for publication)