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In signal processing for high density magnetic recording systems, it is important to combine a signal detection method and an error correction scheme. Error correcting codes for magnetic recording channels are required to be easily implemented and to have high code rates. High dimensional parity check codes with high code rates satisfy these requirements. We show the error correcting performance of the high dimensional parity check codes with high code rates when we apply them to PR channels. We also show that the integrated interleaving ECC technique is useful for a PR channel.