On the design of efficient constrained parity-check codes for optical recording

This paper proposes a general and systematic way to efficiently combine constrained codes with parity-check (PC) codes for optical recording. The proposed constrained PC code includes two component codes: the normal constrained (NC) code and the parity-related constrained (PRC) code. They are designed based on the same finite state machine (FSM). The code rates are only a few tenths below the theoretical maximum. The parity-check constraint is defined by the generator matrix (or generator polynomial) of a linear binary PC code, which can detect any type of dominant error events as well as error event combinations of the system. Two approaches are proposed to design the code in the non-return-to-zero-inverse (NRZI) format and the non-return-to-zero (NRZ) format, respectively. Designing the codes in NRZ format may reduce the number of parity bits required for error detection and simplify post-processing for error correction. Finally, examples of several newly designed codes and their performances are illustrated