Spin-glass models as error-correcting codes

Abstract

DURING the transmission of information, errors may occur because of the presence of noise, such as thermal noise in electronic signals or interference with other sources of radiation. One wants to recover the information with the minimum error possible. In theory this is possible by increasing the power of the emitter source. But as the cost is proportional to the energy fed into the channel, it costs less to code the message before sending it, thus including redundant 'coding' bits, and to decode at the end. Coding theory provides rigorous bounds on the cost-effectiveness of any code. The explicit codes proposed so far for practical applications do not saturate these bounds; that is, they do not achieve optimal cost-efficiency. Here we show that theoretical models of magnetically disordered materials (spin glasses) provide a new class of error-correction codes. Their cost performance can be calculated using the methods of statistical mechanics, and is found to be excellent. These models can, under certain circumstances, constitute the first known codes to saturate Shannon's well-known cost-performance bounds.