A semi-analytical bivariate Gaussian model of the approximation error impact on the Min-Sum LDPC decoding algorithm

In this paper, a new theoretical model that describes the impact of the approximation error on the decisions taken by LDPC decoders is discussed. In particular, the theoretical model extends previous results and reconstructs the mechanism, by means of which the approximation error alters the decisions of the decoding algorithm, with respect to the decisions taken by the optimal decoding algorithm, namely Log Sum-Product. We focus on the most popular algorithm for LDPC decoding, namely Min-Sum and its also popular modifications, normalized and offset Min-Sum. The model is applied to all of these decoding algorithms, which are actually approximations of the Log Sum-Product. Moreover a method that exploits the output of the proposed model in order to estimate the decoding performance is also proposed. Finally, experimental results prove the validity of both the proposed model and the method, demonstrating the usefulness of this contribution towards achieving accurate decoding behavior prediction without relying on time-consuming simulations.