Performance of ML decoding for ensembles of binary and nonbinary regular LDPC codes of finite lengths
Irina E. Bocharova, Boris D. Kudryashov, Vitaly Skachek · 2017
The Gallager ensembles of binary regular LDPC codes and binary images of nonbinary regular LDPC codes are studied. Recurrent procedure for computing average spectra for these two ensembles is presented. By using the existing bounding techniques, estimates on the error probability of the maximum-likelihood (ML) decoding over an AWGN channel with BPSK signaling for short codes from different ensembles of LDPC codes are obtained. The numerical results show performance of the ML decoding for different code ensembles. Conclusions drawn based on the average code spectra are then verified by near-ML decoding simulations for both randomly selected and the best known short codes. The asymptotic ML decoding thresholds for AWGN and BSC channels are calculated. As expected, codes with the ML decoding performance superior to that of the average code in the ensemble, are easy to find. However, comparison of the the presented results with simulation results for belief propagation (BP) decoding shows that the ML decoding performance should not be used as a target for searching for good iteratively decodable codes.