Principles of Digital Communication and Coding
Principles of Digital Communication and Coding
Information Theory and Reliable Communication
Information Theory and Reliable Communication
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Information, Physics, and Computation
Information, Physics, and Computation
Relations between random coding exponents and the statistical physics of random codes
IEEE Transactions on Information Theory
Universal portfolios with side information
IEEE Transactions on Information Theory
Tight bounds for LDPC and LDGM codes under MAP decoding
IEEE Transactions on Information Theory
Error Exponents of Erasure/List Decoding Revisited Via Moments of Distance Enumerators
IEEE Transactions on Information Theory
Relations between random coding exponents and the statistical physics of random codes
IEEE Transactions on Information Theory
Statistical physics of signal estimation in Gaussian noise: theory and examples of phase transitions
IEEE Transactions on Information Theory
| Hi-index | 754.96 |
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.