Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-11-16
J. Phys. A: Math. Theor. 44 (2011) 085002
Physics
Condensed Matter
Disordered Systems and Neural Networks
24 pages, 4 figures
Scientific paper
10.1088/1751-8113/44/8/085002
We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation analysis characterizing the performance of the ensemble, the distortion rate of lossy data compression and the error exponent of channel coding in Gallager's formalism, are accessible by a generating function of the generalized random energy model. We discuss that the transitions of those exponents observed in the preceding work can be interpreted as phase transitions with respect to the replica number. We also show that the replica symmetry breaking plays an essential role in these transitions.
Obuchi Tomoyuki
Takahashi Kazutaka
Takeda Koujin
No associations
LandOfFree
Statistical mechanical analysis of a hierarchical random code ensemble in signal processing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Statistical mechanical analysis of a hierarchical random code ensemble in signal processing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Statistical mechanical analysis of a hierarchical random code ensemble in signal processing will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-464710