A general construction of constrained parity-check codes for optical recording

Abstract

This paper proposes a general and systematic code design method 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 rates of the designed codes are only a few tenths below the theoretical maximum. The PC 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 or error event combinations of the system. Error propagation due to parity bits is avoided, since both component codes are protected by PCs. 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. Examples of several newly designed codes are illustrated. Simulation results with the Blu-Ray disc (BD) systems show that the new d = 1 constrained 4-bit PC code significantly outperforms the rate 2/3 code without parity, at both nominal density and high density.