Asymptotic estimation of error fraction corrected by binary LDPC code

This paper considers new lower bound on fraction of guaranteed corrected errors while decoding the same binary low-density parity-check (LDPC) codes with constituent single parity-check (SPC) and Hamming codes using the same iterative low-complex hard-decision algorithm as in previous works of V. Zyablov and M. Pinsker in 1975 and V. Zyablov, R. Johannesson and M. Loncar in 2009. The number of decoding iterations, required to correct the errors, is a logarithmic function of the code length. The fraction of guaranteed correctable errors computed numerically for various choices of LDPC code parameters with constituent SPC and Hamming codes shows that proposed lower bound gives the better results than previously known best lower bounds obtained by V. Zyablov and M. Pinsker in 1975 for Gallager's LDPC codes and A. Barg and A. Mazumrad for Hamming code-based LDPC (H-LDPC) codes in 2011. Some of obtained numerical results are represented at the end of the paper to demonstrate these improvements.