DocumentCode :
1178982
Title :
The Generalized Random Energy Model and its Application to the Statistical Physics of Ensembles of Hierarchical Codes
Author :
Merhav, Neri
Author_Institution :
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa
Volume :
55
Issue :
3
fYear :
2009
fDate :
3/1/2009 12:00:00 AM
Firstpage :
1250
Lastpage :
1268
Abstract :
In an earlier work, the statistical physics associated with finite-temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida´s random energy model (REM) of spin glasses, according to which the energy levels of the various spin configurations are independent random variables. The generalized REM (GREM) extends the REM in that it introduces correlations between energy levels in an hierarchical structure. In this paper, we explore some analogies between the behavior of the GREM and that of code ensembles which have parallel hierarchical structures. In particular, in analogy to the fact that the GREM may have different types of phase transition effects, depending on the parameters of the model, then the above-mentioned hierarchical code ensembles behave substantially differently in the various domains of the design parameters of these codes. We make an attempt to explore the insights that can be imported from the statistical mechanics of the GREM and be harnessed to serve for code design considerations and guidelines.
Keywords :
hierarchical systems; random codes; statistical analysis; GREM; error exponents; generalized random energy model; hierarchical codes; parallel hierarchical structures; phase transition effects; statistical mechanics; Block codes; Capacity planning; Decoding; Energy states; Glass; Guidelines; Information analysis; Information theory; Physics; Random variables; Error exponents; generalized random energy model (GREM); phase transitions; random coding; spin glasses;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2008.2011445
Filename :
4787614
Link To Document :
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