Name
Title | ||
|---|---|---|
Discrete-Input Two-Dimensional Gaussian Channels With Memory: Estimation and Information Rates Via Graphical Models and Statistical Mechanics |
Abstract | ||
|---|---|---|
Discrete-input two-dimensional (2D) Gaussian channels with memory represent an important class of systems, which appears extensively in communications and storage. In spite of their widespread use, the workings of 2D channels are still very much unknown. In this work, we try to explore their properties from the perspective of estimation theory and information theory. At the heart of our approach is a mapping of a 2D channel to an undirected graphical model, and inferring its a posteriori probabilities (APPs) using generalized belief propagation (GBP). The derived probabilities are shown to be practically accurate, thus enabling optimal maximum a posteriori (MAP) estimation of the transmitted symbols. Also, the Shannon-theoretic information rates are deduced either via the vector-wise Shannon-McMillan-Breiman (SMB) theorem, or via the recently derived symbol-wise Guo-Shamai-Verdu (GSV) theorem. Our approach is also described from the perspective of statistical mechanics, as the graphical model and inference algorithm have their analogues in physics. Our experimental study, based on common channel settings taken from cellular networks and magnetic recording devices, demonstrates that under nontrivial memory conditions, the performance of this fully tractable GBP estimator is almost identical to the performance of the optimal MAP estimator. It also enables a practically accurate simulation-based estimate of the information rate. Rationalization of this excellent performance of GBP in the 2-D Gaussian channel setting is addressed. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/TIT.2008.917638 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
statistical mechanics,excellent performance,gaussian channel,discrete-input two-dimensional gaussian channels,information rates via graphical,information theory,2-d gaussian channel setting,estimation theory,common channel setting,tractable gbp estimator,shannon-theoretic information rate,accurate simulation-based estimate,information rate,probability,maximum a posteriori estimation,graphical models,physics,intersymbol interference,maximum likelihood estimation,belief propagation,graphical model,heart | Information theory,Discrete mathematics,Computer science,A priori and a posteriori,Communication channel,Algorithm,Posterior probability,Artificial intelligence,Maximum a posteriori estimation,Estimation theory,Graphical model,Estimator | Journal |
Volume | Issue | ISSN |
54 | 4 | 0018-9448 |
Citations | PageRank | References |
28 | 1.61 | 23 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ori Shental | 1 | 129 | 14.09 |
| N. Shental | 2 | 181 | 10.40 |
| S. Shamai (Shitz) | 3 | 41 | 3.07 |
| Ido Kanter | 4 | 97 | 13.92 |
| A. J. Weiss | 5 | 684 | 106.42 |
| Yair Weiss | 6 | 10240 | 834.60 |