Low-density parity-check codes with variable rate and randomized constraints for advanced magnetic tape recording

Variable rate and randomized run length limited (VR² RLL) constraint is used in some magnetic tape recording systems. The variable rate encoding algorithm monitors the incoming data stream for conditions such as run length limit (RLL) constraints. If one of the conditions is violated, a bit is inserted into the data stream. The purpose of the VR² RLL constraint is to ensure that the encoded data contains adequate tracking and amplitude information for reliable data detection and prevent the preamble pattern from occurring during the data field. Although the VR² approach to RLL constraint is effective, it has the disadvantages of variable block length and error propagation. Furthermore, VR² is not suitable for soft decision decoding needed by low-density parity check (LDPC) codes being investigated because of their good performance, low complexity and inherent parallel decoding architecture. LDPC codes usually exhibit excellent error correction performance and the LDPC decoder may be able to recover the codeword even if we deliberately introduce some errors in the codeword in order to satisfy RLL constraints. Based on this observation, the paper proposes a scheme of combining LDPC codes with the VR² RLL constraint based on bit flipping. In addition to providing soft decision decoding to achieve large coding gain, the proposed scheme has the advantages of no error propagation and fixed block length.