Spatially Coupled Codes Optimized for Magnetic Recording Applications

Abstract

Spatially coupled (SC) codes are a class of sparse graph-based codes known to have capacity-approaching performance. SC codes are constructed based on an underlying low-density parity-check (LDPC) code, by first partitioning the underlying block code and then putting replicas of the components together. Significant recent research efforts have been devoted to the asymptotic, ensemble-averaged study of SC codes, as these coupled variants of the existing LDPC codes offer excellent properties. While the asymptotic analysis is important, due to simplifying assumptions and averaging effects, results from the asymptotic domain are not readily translatable to the practical, finite-length setting. Despite this chasm, the finite-length analysis of SC codes is still largely unexplored. In this paper, we tackle the problem of optimized design of SC codes in the context of magnetic-recording (MR) applications. In particular, we identify combinatorial structures in the graphical representation of the code that are detrimental in the MR setting. An intriguing observation is that for the same SC code, the problematic objects for the MR channels are combinatorially different from the additive white Gaussian noise (AWGN) setting, thus necessitating a careful code design approach for the MR applications. We first demonstrate that the choice of the so-called cutting vector, which guides the code partitioning in the SC code design, directly affects the cardinality of these problematic objects. In particular, we show that the number of problematic objects is the highest - and consequently that the performance is the worst - in the case of the degenerate cutting vector, which precisely corresponds to uncoupled LDPC block codes. We, therefore, show that coupling always improves the performance and that the degree of improvement is dependent on the choice of the cutting vector. We then extend our analysis to different column weights and present SC codes that outperform block codes with unoptimized edge weights by more than 3.5 orders of magnitude and that also outperform both optimized block codes and unoptimized SC codes by more than two orders of magnitude. Through presented examples, we demonstrate high performance of the proposed code design methodology.