Low Density Parity Check Codes for Channels with Memory

近年来，低密度奇偶校验(LDPC)码被证明具有在无记忆通信信道的香农信道容量的千分之一分贝内执行的能力。这个项目试图回答一个自然的问题：这些代码在有记忆的频道上传输有多好？正在考虑的通道是马尔可夫记忆通道，包括记忆依赖和独立于被传输符号的两个通道。LDPC码的分析和设计得益于将这些码表示为图，其中译码是通过沿着图的边传递消息来完成的。这个图模型允许使用支持最新进展的鞅进行分析，包括密度进化设计技术。研究人员研究如何将这种图形建模方法扩展到有记忆的频道。具体地说，该项目分为四个主要任务：设计新信道模型下的密度进化算法；评估噪声容忍门限；设计短块长度工程码和快速译码；以及利用低密度奇偶校验码实现频谱整形。

In recent years, low-density parity-check (LDPC) codes have been shownto have the power to perform within thousandths of decibels of theShannon channel capacity of memoryless communications channels. Thisproject seeks to answer a natural question: how good are these codesfor transmission over channels with memory? The channels underconsideration are Markovian memory channels, including both channelswhere the memory is dependent and independent of the transmittedsymbols. Such channels arise in several applications, such as diskdrives or other storage media.The analysis and design of LDPC codes has benefited from representingthese codes as graphs, where the decoding is done by passing messagesalong the graph edges. This graph model allows an analysis usingmartingales that underlies recent advances, including the densityevolution design technique. The investigators study how to extendthis graphical modeling approach to channels with memory. Morespecifically, the project is divided into four major tasks: designing density evolution algorithms under new channel models;evaluating noise tolerance thresholds; engineering codes for shortblock lengths and rapid decoding; and achieving spectral shaping withlow-density parity-check codes.