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The extrinsic information transfer (EXIT) functions of Hadamard codes in the context of repeat-zigzag-Hadamard (RZH) codes with parallel decoding are investigated. EXIT functions over both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise (BIAWGN) channel are derived. The application of these EXIT functions in the design of low-rate capacity-approaching irregular RZH (IRZH) codes is also considered. Using the EXIT functions, the bit error rate (BER) for a given code profile can be easily estimated and the differential evolution (DE) technique can be employed to find the optimal degree profile for given design parameters. The EXIT functions derived in this communication can serve as an effective tool for designing low-rate IRZH codes with parallel decoding in both BEC and BIAWGN channels.