Europhysics Letters

(received ; accepted) PACS. 89.90+n { Other areas of general interest to physicists. Abstract. { 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 nite. Close to optimal error-correcting capability is obtained for nite K and C. We examine the nite temperature case to assess the use of simulated annealing for decoding and extend the analysis to accommodate other types of noisy channels. Error-correcting codes are of signiicant practical importance as they provide mechanisms for retrieving the original message after possible corruption due to noise during transmission. They are being used extensively in most means of information transmission from satellite communication to the storage of information on hardware devices. The coding eeciency, measured in the percentage of informative transmitted bits, plays a crucial role in determining the speed of communication channels and the eeective storage space on hard-disks. Rigorous bounds 1] have been derived for the maximal channel capacity for which codes, capable of achieving arbitrarily small error probability, can be found. However, existing practical error-correcting codes do not saturate this bound and the quest for more eecient error-correcting codes has been going on ever since. A new family of error-correcting codes, based on insights gained from the statistical mechanical analysis of Ising spin models, has recently been suggested by Sourlas 2], instigating the use of statistical mechanics for constructing and investigating novel coding methods 3, 4]. However, the codes suggested and analyzed so far are of no practical signiicance as they imply an innnite ratio between the length of the transmitted word and the original message. Consequently, they had little impact on the design and the understanding of practical codes.