Open AccessNew explicitly invertible approximation of the function involved in LDPC codes density evolution analysis using a Gaussian approximation
Author(s) -
Vatta F.,
Soranzo A.,
Comisso M.,
Buttazzoni G.,
Babich F.
Publication year - 2019
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
ISSN - 1350-911X
DOI - 10.1049/el.2019.1349
Subject(s) - low density parity check code , invertible matrix , mathematics , decoding methods , gaussian , piecewise , function (biology) , inverse , convergence (economics) , probability density function , algorithm , discrete mathematics , mathematical analysis , statistics , pure mathematics , physics , geometry , quantum mechanics , evolutionary biology , economics , biology , economic growth
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 ϕ ( x ) , therein specified, and its inverse. In this Letter, a new approximation of the function ϕ ( 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.