Run-length limited parity-check coding for transition-shift errors in optical recording

Random channel errors that may occur in the run-length limited (RLL) channel bit-stream after bit-detection, are commonly repaired by error correction (de)coding (ECC) after demodulation of the RLL bit-stream. RLL parity-check coding makes it possible to correct random errors already at the level of the channel bit-stream, at a much lower overhead than needed for standard ECC. With parity-check coding, a certain parity-check constraint is realized on segments of the RLL channel bit-stream. Violation of the parity-check constraint in the as-detected RLL bit-stream enables error detection; for error correction, some side information from the channel waveform is needed. One scheme from the literature considers parsing of parity-check blocks into the original RLL bit-stream. Another scheme is concatenated parity-check coding. While the parsing scheme has the drawback of low coding efficiency, its advantage is its simplicity and the lack of error propagation. The concatenated scheme has a high efficiency but it suffers from error propagation, and local demodulation is needed to derive the parity checks. As an alternative solution, we propose to use a parity-check coding scheme based on a combination of codes. Such a scheme is called 'combi-code', a term that was proposed within the frame-work of DC-free RLL codes. Apart from a main RLL code, a second RLL code, the parity-check enabling code, is required. The latter code is used to set the parity-check constraint of a segment to a predetermined value. Parity-check coding via combi-codes combines the advantages of the two other schemes: simplicity, a high coding efficiency, and no error propagation.