Critical Noise Levels for LDPC decoding
J. van Mourik, D. Saad, Y. Kabashima
Abstract
We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator (), rather than on the weight enumerator () employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.
Create a lesson
Related papers
Attention over noisy examples: generalization and memorization in the exponential Hopfield network
Francesco Alemanno
Finite-size geometric crossover toward fragmentation of the potential energy shell in the quantum random energy model
Ishita Modak, Vatsana Tiwari, Soumya Bera
Testing Replica Symmetry Breaking in the three-dimensional Edwards-Anderson model by using vanishing fields
Miguel Aguilar-Janita, Silvio Franz, Victor Martin-Mayor et al.
Deep Learning of Phase Transitions for Bilinear-Biquadratic Spin-1 Chains from Correlation Aspects
Ming-Chiang Chung, Yu-Ting Kuo, Ian McCulloch et al.
Resolving Structural Uncertainty in Stochastic Dynamical Systems via Ensemble-Based Bayesian Inference
Francesco Zambelli, Valeria D'Andrea, Manlio De Domenico
Seismology of Glasses
Zhiyu Cao, Peter G. Wolynes