Finite-size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

[1]  David J. C. MacKay,et al.  Comparison of constructions of irregular Gallager codes , 1999, IEEE Trans. Commun..

[2]  Claude E. Shannon,et al.  A mathematical theory of communication , 1948, MOCO.

[3]  Brendan J. Frey,et al.  Graphical Models for Machine Learning and Digital Communication , 1998 .

[4]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[5]  Allen H. Levesque,et al.  Error-control techniques for digital communication , 1985 .

[6]  D. Saad,et al.  Error-correcting codes that nearly saturate Shannon's bound , 1999, cond-mat/9906011.

[7]  D. B. Saakian,et al.  Diluted generalized random energy model , 1998 .

[8]  Kanter,et al.  Cascading parity-check error-correcting codes , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Nicolas Sourlas,et al.  Spin-glass models as error-correcting codes , 1989, Nature.

[10]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[11]  Radford M. Neal,et al.  Near Shannon limit performance of low density parity check codes , 1996 .

[12]  Yair Weiss,et al.  Correctness of Local Probability Propagation in Graphical Models with Loops , 2000, Neural Computation.

[13]  Kanter.  Asymmetric neural networks with multispin interactions. , 1988, Physical review. A, General physics.

[14]  Saad,et al.  Typical performance of gallager-type error-correcting codes , 2000, Physical review letters.

[15]  D. Saad,et al.  Statistical mechanics of error-correcting codes , 1999 .

[16]  Kanter,et al.  Mean-field theory of spin-glasses with finite coordination number. , 1987, Physical review letters.

[17]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .