CAREER: Information Theory and Iterative Decoding for Channels With Memory

这项研究的主旨是为数字信息的传输和存储开发创新的新技术。数字信息的存储和传输现在在我们的社会中是如此无处不在，以至于提高这一领域的技术水平具有连锁反应，可以促进许多其他领域的进步。随着这项技术被推向极限，需要越来越复杂的模型来准确地表示通信系统。为此，本研究集中于高级系统模型，其特性依赖于系统先前的输入和输出。硬盘驱动器是这些复杂系统的一个很好的代表，这项研究将有助于提高未来磁存储系统的容量和可靠性。本研究主题的统一主题是一类被称为有限状态通道(FSCS)的通信通道(有记忆)。FSC是一类非常通用的信道，用于对包括相关衰落信道、码间干扰信道和磁记录信道在内的复杂信道进行建模。这项研究的第一部分考虑了信息量的实际计算，如容量和错误指数，这些量对于设计故障率非常低的磁存储设备非常重要。第二部分涉及FSCS和低密度奇偶校验(LDPC)码的联合迭代译码。特别是，这项工作考虑了联合译码的伪码字分析，该分析可用于优化有限块长度的代码。第三部分研究有限态源的率失真问题，描述这种大失真的率失真曲线一直是信息论中的一个公开问题。

The main thrust of this research is the development of innovative new techniques for the transmission and storage of digital information. The storage and transmission of digital information is now so ubiquitous in our society, that improving the state of the art in this area has a ripple effect that can enable advances in many other fields. As this technology is pushed to its limits, increasingly complex models are required to represent communication systems accurately. To this end, this research focuses on advanced system models whose properties depend on previous inputs and outputs from the system. Hard disk drives are a good representative of these complicated systems and this research should help improve the capacity and reliability of future magnetic storage systems.The unifying theme of this research theme is a class of communication channels (with memory) known as finite-state channels (FSCs). FSCs are a very general class of channels that are used to model complex channels including correlated fading channels, inter-symbol interference channels, and magnetic recording channels. The first part of this research considers the practical computation of information-theoretic quantities, such as the capacity and the error exponent, that are important for the design of magnetic storage devices with very low failure rates. The second part involves the joint iterative decoding for FSCs and low-density parity-check (LDPC) codes. In particular, this work considers a pseudo-codeword analysis for joint decoding that can be used to optimize codes for finite block lengths. The third part studies the rate-distortion (RD) problem for finite-state sources; characterizing this RD curve for large distortions has long been an open problem in information theory.