Statistical mechanics of error-correcting codes
Yoshiyuki Kabashima, David Saad · Europhysics Letters (EPL) · 1999
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.