New explicitly invertible approximation of the function involved in LDPC codes density evolution analysis using a Gaussian approximation

Low density parity check (LDPC) codes are still intensively studied investigating their iterative decoding convergence performance. Since the probability distribution function of the decoder's log-likelihood ratio messages was observed to be approximately Gaussian, a variety of low-complexity approaches to this investigation were proposed. One of them was presented in Chung et al.'s 2001 paper, involving the function f(x), therein specified, and its inverse. In this Letter, a new approximation of the function f(x) is given, such that, unlike the other approximations found in the literature, it is defined by a single expression (i.e. it is not piecewise defined), it is explicitly invertible, and it has less relative error in any x than the other approximations.