Upper Bounds on the Error Exponents of LDPC Code Ensembles

We consider the ensemble of regular LDPC codes and use recent concentration results on the distance spectrum to derive upper bounds on the error exponent of a randomly chosen code from the ensemble. These bounds hold with some confidence level that approaches one as the connectivity of the graph increases. We show that the bounds can be used to obtain the true error exponent over some range of channel parameter values, with the above confidence level