Information Geometry and Low Density Parity Check Codes

The application of information geometry in the low density parity check (LDPC) codes based on the work of Ikeda and Amari is considered. The method is to turn the decoding process into the change of the parameter. When the LDPC decoding procedure converges, both the convergent probability distribution and the true probability distribution belong to the same submanifold, but this does not mean they are equimarginal, that points out the origin of the decoding error.