Statistical mechanics of error-correcting codes
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology - Yokohama 226, Japan
2 The Neural Computing Research Group, Aston University, Birmingham B4 7ET, UK
Accepted: 9 October 1998
We investigate the performance of error-correcting codes, where the code word comprises products of K bits selected from the original message and decoding is carried out utilizing a connectivity tensor with C connections per index. Shannon's bound for the channel capacity is recovered for large K and zero temperature when the code rate K/C is finite. Close to optimal error-correcting capability is obtained for finite K and C. We examine the finite-temperature case to assess the use of simulated annealing for decoding and extend the analysis to accommodate other types of noisy channels.
PACS: 89.90.+n – Other areas of general interest to physicists / 89.70.+c – Information science / 05.50.+q – Lattice theory and statistics; Ising problems
© EDP Sciences, 1999