Stochastic reasoning, free energy, and information geometry
Neural Computation
Iterative decoding of concatenated codes: a tutorial
EURASIP Journal on Applied Signal Processing
On the Minima of Bethe Free Energy in Gaussian Distributions
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Accuracy of Loopy belief propagation in Gaussian models
Neural Networks
A multiclass classification method based on decoding of binary classifiers
Neural Computation
IEEE Transactions on Information Theory
Data extraction from wireless sensor networks using distributed fountain codes
IEEE Transactions on Communications
Theoretical analysis of accuracy of Gaussian belief propagation
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Belief propagation, Dykstra's algorithm, and iterated information projections
IEEE Transactions on Information Theory
| Hi-index | 754.96 |
Since the proposal of turbo codes in 1993, many studies have appeared on this simple and new type of codes which give a powerful and practical performance of error correction. Although experimental results strongly support the efficacy of turbo codes, further theoretical analysis is necessary, which is not straightforward. It is pointed out that the iterative decoding algorithm of turbo codes shares essentially similar ideas with low-density parity-check (LDPC) codes, with Pearl's belief propagation algorithm applied to a cyclic belief diagram, and with the Bethe approximation in statistical physics. Therefore, the analysis of the turbo decoding algorithm will reveal the mystery of those similar iterative methods. In this paper, we recapture and extend the geometrical framework initiated by Richardson to the information geometrical framework of dual affine connections, focusing on both of the turbo and LDPC decoding algorithms. The framework helps our intuitive understanding of the algorithms and opens a new prospect of further analysis. We reveal some properties of these codes in the proposed framework, including the stability and error analysis. Based on the error analysis, we finally propose a correction term for improving the approximation.