On the Error-Correcting Capabilities of Low-Complexity Decoded LDPC Codes with Constituent Hamming Codes

In English Hamming code-based LDPC (H-LDPC) block codes are obtained by replacing the single parity-check constituent codes in Gallager's LDPC codes with Hamming codes. This paper investigates the asymptotic performance of ensembles of random H-LDPC codes, used over the binary symmetric channel and decoded with a low-complexity hard-decision iterative decoding algorithm. It is shown that there exist H-LDPC codes for which such iterative decoding corrects any error pattern with a number of errors that
grows linearly with the code length. The number of required decoding iterations is a logarithmic function of the code length. The fraction of correctable errors is computed numerically for different code parameters.