2011年2月
Statistical mechanical analysis of a hierarchical random code ensemble in signal processing
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- ,
- ,
- 巻
- 44
- 号
- 8
- 開始ページ
- 085002
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1088/1751-8113/44/8/085002
- 出版者・発行元
- IOP PUBLISHING LTD
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.
- リンク情報
- ID情報
-
- DOI : 10.1088/1751-8113/44/8/085002
- ISSN : 1751-8113
- ORCIDのPut Code : 51566777
- Web of Science ID : WOS:000287138400002
- ORCIDで取得されたその他外部ID : a:1:{i:0;a:1:{s:14:"source-work-id";s:12:"CTT100718221";}}