LDPC Codes with Local and Global Decoding

TL;DR

This paper introduces LDPCL codes that enable efficient local and global decoding for storage, providing a theoretical framework and design tools to optimize error correction and capacity achievement with trade-offs.

Contribution

It develops a novel theoretical framework and design methodology for LDPC codes with local and global decoding capabilities, supporting capacity achievement.

Findings

Design tool for LDPC codes with local/global levels

Capacity can be achieved with the proposed codes

Trade-off between locality and error correction performance

Abstract

This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or locally when a smaller sub-block is accessed (to reduce latency). LDPCL codes are designed to maximize the error-correction performance vs. rate in the usual (global) mode, while at the same time providing a certain performance in the local mode. We develop a theoretical framework for the design of LDPCL codes. Our results include a design tool to construct an LDPC code with two data-protection levels: local and global. We derive theoretical results supporting this tool and we show how to achieve capacity with it. A trade-off between the gap to capacity and the number of full-block accesses is studied, and a finite-length analysis of ML decoding is performed to exemplify a trade-off between the locality capability and the full-block error-correcting capability.