On the EXIT chart analysis of low-density parity-check codes

The extrinsic information transfer (EXIT) charts are used to analyze the sum-product decoding algorithm of low-density parity-check (LDPC) codes. The codes are optimized by performing curve fitting on EXIT charts. This technique is developed for binary erasure channels based on area property and is extended to other channels. We show that on channels where the area property is not valid, the curve fitting approach is a sub-optimal method of optimizing for the best convergence threshold. On Gaussian channels, the messages from variable nodes to check nodes are approximated by a symmetric Gaussian distribution. We prove that the check node detector mutual information transfer function derived using this approximation is an upper bound. So the EXIT chart analysis predicts an optimistic value for the convergence threshold. We give an empirical lower bound for the check node detector mutual information transfer function. For few irregular LDPC codes designed for AWGN channel using density evolution, we have examined the accuracy of convergence thresholds predicted by EXIT charts using these bounds for the check node transfer function. The analysis of EXIT chart technique presented in this paper can be extended to other channels for which the distribution of channel messages can be approximated by a symmetric Gaussian/Gaussian mixture distribution.