Digitale Medien
Springer
The European physical journal
23 (2001), S. 121-136
ISSN:
1434-6036
Schlagwort(e):
PACS. 75.10.Hk Classical spin models – 75.10.Nr Spin-glass and other random models – 89.70.+c Information science
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Physik
Notizen:
Abstract: Gallager codes are the best error-correcting codes to date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be solved by elementary methods (i.e. without replicas) in a large connectivity limit. For low enough temperatures it presents a completely frozen glassy phase (q EA = 1). The same scenario is shown to hold for finite connectivities. In this case we adopt the replica approach and exhibit a one-step replica symmetry breaking order parameter. We argue that our ansatz yields the exact solution of the model. This allows us to determine the whole phase diagram and to understand the performances of Gallager codes.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/s100510170089
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