Issue |
Europhys. Lett.
Volume 51, Number 6, September II 2000
|
|
---|---|---|
Page(s) | 698 - 704 | |
Section | Interdisciplinary physics and related areas of science and technology | |
DOI | https://doi.org/10.1209/epl/i2000-00395-x | |
Published online | 01 September 2002 |
Error-correcting code on a cactus: A solvable model
1
The Neural Computing Research Group, Aston University - Birmingham B4 7ET, UK
2
Department of Computational Intelligence and Systems Science
Tokyo Institute of Technology, Yokohama 2268502, Japan
Received:
10
May
1999
Accepted:
21
July
2000
An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.
PACS: 89.90.+n – Other topics of general interest to physicists / 89.70.+c – Information science / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, 2000
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