2-D LDPC Codes and Joint Detection and Decoding for Two-Dimensional Magnetic Recording

Abstract

Two-dimensional magnetic recording (TDMR) is a promising technology for boosting areal densities using sophisticated signal processing algorithms within a systems framework. The read/write channel architectures have to effectively tackle 2D inter-symbol interference (ISI), 2D synchronization errors, media and electronic noise sources as well as thermal asperities resulting in burst erasures. 1D low-density parity check (LDPC) codes are well studied to correct large 1D burst errors/erasures. However, such 1D LDPC codes are not suitable for correcting 2D burst errors/erasures due to the 2D span of errors. In this paper, we propose construction of a native 2D LDPC code to effectively correct 2D burst erasures. We also propose a joint detectiondecoding engine based on the generalized belief propagation (GBP) algorithm to simultaneously handle 2D ISI, as well as correct bit/burst errors for TDMR channels. Our work is novel in two aspects: (a) We propose the construction of native 2D LDPC codes to correct large 2D burst erasures, (b) We develop a 2D joint signal detection-decoder engine that incorporates 2D ISI constraints, modulation code constrains along with LDPC decoding. The native 2D LDPC code can correct > 20% more burst erasures compared to the 1D LDPC code over a 2D page of detected bits. Also, the proposed algorithm is observed to achieve a signal-to-noise ratio (SNR) gain of > 0.5 dB in bit error rate (BER) performance (translating to 10% increase in areal densities around the 1.8 Tb/in 2 regime with grain sizes of 9 nm) as compared to a decoupled detector-decoder system configuration. The efficacy of our proposed algorithm and system architecture is evaluated by assessing areal density (AD) gains via simulations for a TDMR configuration comprising of a 2D generalized partial response (GPR) over the Voronoi media model assuming perfect 2D synchronization.

A Log-Likelihood Ratio based Generalized Belief Propagation

“…The GBP algorithm is employed to provide an approximate solution to the problem of minimizing the Gibbs free energy [7], [19]. This algorithm is empirically observed to provide marginal probability estimates, close to true marginal probabilities [20], [21]. The main characteristic of GBP is represented by the fact that messages are passed between clusters of variable nodes, along the region graph.…”

Evaluation of a Joint Detector Demodulator Decoder (JDDD) Performance With Modulation Schemes Specified in the DVB-S2 Standard

“…In the usual IDD, detection is performed on a trellis, while decoding is performed on a Tanner graph [14] using the belief-propagation algorithm (BPA). In order to achieve the detection and decoding operations jointly, one could take the approach in [18], [20], in which they convert the detector to operate over a Tanner graph and use the BPA to perform both the detection and decoding. With the JDDD we are taking, in a sense, the opposite approach, where we convert the algorithm to operate entirely over a trellis.…”