On the Error Exponents of Capacity Approaching Construction of LDPC code

In this paper we consider low-density parity-check (LDPC) codes with special construction. We obtain the lower-bounds on the error exponents for these codes under proposed low-complexity decoding algorithm and under a well known maximum likelihood decoding algorithm. We show that such LDPC code with special construction exists, that the error probability of the low-complexity decoding algorithm exponentially decreases with the code length for all code rates below the channel capacity. We also show that obtained lower-bound on the error exponent under the maximum likelihood decoding almost reaches the lower-bound on the error exponent of good linear codes under the maximum likelihood decoding. The error exponents are computed numerically for different code parameters.