Multi-Dimensional Spatially-Coupled Code Design Through Informed Relocation of Circulants

TL;DR

This paper introduces a systematic framework for designing multi-dimensional spatially-coupled codes with improved girth and error performance by optimally relocating problematic circulants, benefiting high-density data storage systems.

Contribution

It presents a novel method for constructing multi-dimensional SC codes with better girth properties through informed circulant relocation and power adjustment.

Findings

Up to 85% reduction in smallest cycle population.

Up to 3.8 orders of magnitude BER improvement.

Enhanced robustness in data storage applications.

Abstract

A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this paper, we present a systematic framework for constructing MD-SC codes with notably better girth properties than their 1D-SC counterparts. In our framework, informed multi-dimensional coupling is performed via an optimal relocation and an (optional) power adjustment of problematic circulants in the constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are demonstrated to have up to 85% reduction in the population of the smallest cycle, and up to 3.8 orders of magnitude BER improvement in the early error floor region. The results of this work can be particularly beneficial in data storage systems, e.g., 2D magnetic recording and 3D Flash systems, as high-performance MD-SC codes are robust against various channel impairments and non-uniformity.