Estimation of the exponent of the decoding error probability for a special generalized LDPC code

A special construction of a generalized low-density parity-check (LDPC) code and a low-complexity algorithm for his code decoding are proposed. A lower estimate of the exponent of the decoding error probability is obtained for the considered code and the decoding algorithm. This estimate leads the conclusion that, in an ensemble of considered LDPC codes, there are codes with rates as high as the code capacity and the exponent of the decoding error probability exceeds zero.