  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.
  I will also show how the recently discovered (or rediscovered) capacity
approaching codes (turbo codes and low density parity check codes) can be
analysed using statistical mechanics. It is possible to show, using statistical
mechanics, that these codes allow error-free communication for signal to noise
ratio above a certain threshold. This threshold depends on the particular code,
and can be computed analytically in many cases.
