Impact of Approximation Error on the Decisions of LDPC Decoding

Abstract

In this paper the impact of the approximation error on the decisions taken by LDPC decoders is studied. In particular, we analyze the mechanism, by means of which approximation error alters the decisions of a finite-word-length implementation of the decoding algorithm, with respect to the decisions taken by the infinite precision case, approximated here by double-precision floating-point. We focus on four popular algorithms for LDPC decoding, namely Log Sum-Product, Min-Sum, normalized Min-Sum and offset Min-Sum. A corresponding theoretical model is developed which derives an expression for the probability of altering the decision due to approximation. The model is applied to the above algorithms for the case of the first iteration as well as for higher numbers of iterations. Finally, experimental results prove the validity of the proposed model.