On the Decoding Performance of Spatially Coupled LDPC Codes with Sub-block Access

TL;DR

This paper introduces a theoretical framework for analyzing the decoding performance of spatially coupled LDPC codes when only sub-blocks are accessed, enabling efficient decoding in data storage applications.

Contribution

It develops a methodology to derive semi-global decoding thresholds from single-sub-block graph thresholds for spatially coupled LDPC codes.

Findings

Semi-global decoding thresholds can be derived from single-sub-block graph thresholds.

Lower bounds on decoder performance are established for channels with sub-block variability.

The framework applies to data-storage scenarios with partial code access.

Abstract

We study spatially coupled LDPC codes that allow access to sub-blocks much smaller than the full code block. Sub-block access is realized by a semi-global decoder that decodes a chosen target sub-block by only accessing the target, plus a prescribed number of helper sub-blocks adjacent in the code chain. This paper develops a theoretical methodology for analyzing the semi-global decoding performance of spatially coupled LDPC codes constructed from protographs. The main result shows that semi-global decoding thresholds can be derived from certain thresholds we define for the single-sub-block graph. These characterizing thresholds are also used for deriving lower bounds on the decoder's performance over channels with variability across sub-blocks, which are motivated by applications in data-storage.