Finite-size effects and error-free communication in Gaussian channels

The efficacy of st specially constructed Gallager-type, error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in bath encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.