Low Density Parity Check Codes for Channels with Memory

Harvard University, Cambridge MA

Investigators

Abstract

In recent years, low-density parity-check (LDPC) codes have been shown to have the power to perform within thousandths of decibels of the Shannon channel capacity of memoryless communications channels. This project seeks to answer a natural question: how good are these codes for transmission over channels with memory? The channels under consideration are Markovian memory channels, including both channels where the memory is dependent and independent of the transmitted symbols. Such channels arise in several applications, such as disk drives or other storage media. The analysis and design of LDPC codes has benefited from representing these codes as graphs, where the decoding is done by passing messages along the graph edges. This graph model allows an analysis using martingales that underlies recent advances, including the density evolution design technique. The investigators study how to extend this graphical modeling approach to channels with memory. More specifically, the project is divided into four major tasks: designing density evolution algorithms under new channel models; evaluating noise tolerance thresholds; engineering codes for short block lengths and rapid decoding; and achieving spectral shaping with low-density parity-check codes.