On Estimation of the Error Exponent for Finite Length Regular Graph-Based LDPC Codes

Abstract

The error exponent of the regular graph-based binary low-density parity-check (LDPC) codes under the maximum likelihood (ML) decoding algorithm in the binary symmetric channel (BSC) is analyzed. Unlike most other papers where error exponents are considered for the case when the length of LDPC codes tends to infinity (asymptotic analysis), the finite length case (finite length analysis) is considered. In this paper, a method of deriving the lower bound on the error exponent for a regular graph-based LDPC code with finite length under ML decoding is described. Also we analyze Dependences of the error exponent on various LDPC code parameters are also analyzed. The numerical results obtained for the considered lower bound are represented and analyzed at the end of the paper.