Typical coding schemes for magnetic or optical recording usually consist of two coding stages, error correcting coding (ECC) followed by line or modulation coding. Two methods are presented to design a line code with error correcting capability. Both methods modify the linear error-correcting codes so that they satisfy the runlength constraints of runlength-limited (RLL) sequences. Through these methods we construct combined ECC/RLL codes with different runlengths. The first method utilizes a linear combination of ECC codewords with a modification vector. The second method uses a two-dimensional code to design the required ECC/RLL code. Both methods are basically dependent on binary operations and minor changes to the ECC coding/decoding circuitry are required. An asymptotic upper bound on the maximum runlength for both methods is found and the performance of the proposed ECC/RLL codes with conventional multistage cascaded schemes of ECC and RLL is also studied.
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