Multistage coding for data storage systems

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