Spatially Coupled LDPC Codes with Sub-Block Locality

TL;DR

This paper introduces SC-LDPCL codes that enable local decoding of sub-blocks in storage systems, balancing local and global error correction, with analysis of semi-global decoding and performance bounds under variable channels.

Contribution

It presents a novel class of spatially coupled LDPC codes with sub-block locality, allowing flexible local and global decoding, and provides density-evolution analysis and performance bounds.

Findings

SC-LDPCL codes enable local decoding at sub-block level.

Trade-offs between local and global correction are controllable.

Performance bounds are derived for variable channel conditions.

Abstract

A new type of spatially coupled low-density parity-check (SC-LDPC) codes motivated by practical storage applications is presented. SC-LDPCL codes (suffix 'L' stands for locality) can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus offering flexible access to the coded information alongside the strong reliability of the global full-block decoding. Toward that, we propose constructions of SC-LDPCL codes that allow controlling the trade-off between local and global correction performance. In addition to local and global decoding, the paper develops a density-evolution analysis for a decoding mode we call semi-global decoding, in which the decoder has access to the requested sub-block plus a prescribed number of sub-blocks around it. SC-LDPCL codes are also studied under a channel model with variability across sub-blocks, for which decoding-performance lower bounds are derived.