On Accuracy of Gaussian Assumption in Iterative Analysis for LDPC Codes

Iterative analysis for low-density parity-check (LDPC) codes uses the prevailing assumption that messages exchanged between the variable nodes and the check nodes follow a Gaussian distribution. However, the justification is largely pragmatic rather than being based on any rigorous theory. This paper provides a theoretic support by investigating when and how well the Gaussian distribution approximates the real message density and the far subtler why. The analytical results are verified by extensive simulations