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A new analysis of irregular low density parity check (LDPC) codes on AWGN channels based on modified extrinsic information transfer (EXIT) charts is presented. We modify EXIT charts to track the message error rate transfer characteristics of the constituent codes. Previous analyses, which make a Gaussian assumption for all messages passed, are inaccurate at low SNRs. We more accurately track the message error rate transfer by making a Gaussian approximation only for messages sent from variable nodes, with statistics of messages from check nodes computed by simulation. This makes the analysis more accurate, particularly for low rate codes where, at low SNR, the messages from check nodes are far from Gaussian. The new analysis simplifies understanding of the irregular codes to the level of regular case, leading to a simple approach to the design of irregular codes. We have used this method to design irregular LDPC codes that perform close to the Shannon limit over a wider range of rates and variable degrees as compared to previous work. The same method can be used for many other codes defined on graphs.