  I will show that there is a deep relation between error-correction codes and
certain mathematical models of spin glasses. In particular minimum error
probability decoding is equivalent to finding the ground state of the
corresponding spin system. The most probable value of a symbol is related to
the magnetization at a different temperature. Convolutional codes correspond to
one-dimensional spin systems and Viterbi's decoding algorithm to the transfer
matrix algorithm of Statistical Mechanics. A particular spin-glass model, which
is exactly soluble, corresponds to an ideal code, i.e. a code which allows
error-free communication if the rate is below channel capacity.
