Coding and detection for 2-dimensional channels
Coding and detection techniques for one-dimensional (1-D) intersymbol interference (ISI) channels, particularly magnetic and optical recording channels, have been studied extensively for almost three decades. On the modulation coding side, the state-splitting algorithm has been developed to design efficient systematic modulation codes. On the detection side, Viterbi detector and decision-feedback equalization (DFE) have been well-understood. Two-dimensional (2-D) holographic data storage, has been developed to store the information pagewise instead of on 1-D tracks. This will significantly increase the storage density and read/write access of the information.
However, most of the modulation coding and detection techniques for 1-D recording systems are unusable for 2-D holographic data storage. In this work, we present various methods for modelling and equalizing 2-D ISI channels. Some low complexity detectors, such as a threshold detector, have been proposed for certain 2-D ISI channels. One of the main problems of the holographic data storage is the misalignment between written and sampled data pages. This problem is addressed by using more detector pixels than data points, which is called oversampling. We also attempted to characterize the distance properties of certain 2-D ISI channels. An algorithm for finding error events is developed for any 2-D ISI channel.
Unlike the 1-D constrained systems, the capacity of most 2-D constrained systems is not analytically known due to the lack of graph-based descriptions of such channels. This also complicates the design of efficient modulation codes. We propose algorithms for finding single-state and finite-state block codes for the hard-square constraint. The encoding and decoding of the modulation codes can be performed easily using codeword generating templates. We also propose an algorithm for finding single-state block codes for any 2-D constrained system represented by a set of forbidden patterns.
For 1-D recording, we designed block codes satisfying the running digital sum (RDS) and time-varying maximum transition run (TMTR) constraints for perpendicular recording channels. The graphs of these constraints are combined to understand the design trade-off between the achievable coding rate and constraint parameters. The spectra of the combined constraints shows the properties of the constituent constraints. The modulations codes are designed by searching for all codewords satisfying certain constraint properties.