  The generalization of Shannon's theory to include messages with given
autocorrelations is presented. The analytical calculation of the channel
capacity is based on the transfer matrix method of the effective 1D
Hamiltonian. This bridge between statistical physics and information theory
leads to efficient Low-Density Parity-Check Codes over Galois fields that
nearly saturate the channel capacity. The novel idea of the decoder is the
dynamical updating of the prior block probabilities which are derived from the
transfer matrix solution and from the posterior probabilities of the
neighboring blocks. Application and possible extensions are discussed,
specifically the possibility of achieving the channel capacity without
compression of the data.
