LDPC Codes for Partial-Erasure Channels in Multi-Level Memories

TL;DR

This paper introduces the q-ary partial erasure channel (QPEC) model to simulate partial knowledge in multi-level memories and analyzes LDPC codes' performance over this channel using density evolution and threshold analysis.

Contribution

It develops the QPEC model and provides density evolution equations and decoding threshold analysis for LDPC codes on this channel, addressing an open problem in additive combinatorics.

Findings

Density evolution equations for QPEC

Decoding threshold analysis for LDPC codes

Bounds and approximations for the open problem

Abstract

In this paper, we develop a new channel model, which we name the $q$-ary partial erasure channel (QPEC). QPEC has a $q$-ary input, and its output is either one symbol or a set of $M$ possible values. This channel mimics situations when current/voltage levels in measurement channels are only partially known, due to high read rates or imperfect current/voltage sensing. Our investigation is concentrated on the performance of low-density parity-pheck (LDPC) codes when used over this channel, due to their low decoding complexity with iterative-decoding algorithms. We give the density evolution equations of this channel, and develop its decoding-threshold analysis. Part of the analysis shows that finding the exact decoding threshold efficiently lies upon a solution to an open problem in additive combinatorics. For this part we give bounds and approximations.