Fundamental Trade-Offs and Parametric Decoding for LDPC Codes

纠错码是几乎所有数字通信和数据存储系统的关键部分，包括手机、互联网、太空任务和光盘。差错控制编码，也称为信道编码，保护数据不受传输差错的影响，以确保足够的传输质量。具有迭代译码技术的基于图的码（诸如Turbo码和低密度奇偶校验（LDPC）码）的出现彻底改变了信道编码。LDPC码将成为未来通信系统的重要组成部分。尽管LDPC码具有非常好的性能，但其存在重要的问题。这项研究提供了改进的理解和实际实施的LDPC码使用PI介绍的新方法。 研究领域包括1。参数迭代译码：研究了一种新的LDPC码译码方法，称为参数迭代译码。新的解码方法提供了更好的权衡之间的可靠性，带宽使用，和成本比标准的迭代解码。2.实现容量的LDPC码：本文研究了一种基于零速率码和删余的容量可达LDPC码的解析设计方法。 扩展的想法，构建通用的速率自适应LDPC码进行了研究。3. LDPC码的错误平层：这个项目开发了一个严格的框架来回答以下问题：给定一个可接受的错误平层水平，我们可以获得的最佳性能是什么？我们如何才能实现这一业绩？

Error-correcting codes are a critical part of almost all digital communications and data storage systems, including cell phones, the Internet, space missions, and compact disks. Error control coding, also known as channel coding, protects data against transmission errors to ensure adequate transmission quality. The emergence of graph-based codes (such as turbo codes and low-density parity-check (LDPC) codes) with iterative decoding techniques has revolutionized channel coding. It is now clear that LDPC codes will be an essential part of future communication systems. Despite their astonishingly good performance, LDPC codes suffer from important problems. This research provides improvements in understanding and practical implementation of LDPC codes using new approaches introduced by the PI. The areas of research considered are 1. Parametric Iterative Decoding: A novel decoding method for LDPC codes, called parametric iterative decoding, is investigated. The new decoding method provides better trade-offs among reliability, bandwidth usage, and cost than the standard iterative decoding. 2. Capacity-Achieving LDPC Codes: This research studies a new approach to the analytical design of capacity-achieving LDPC codes based on zero-rate codes and puncturing. Extensions of the ideas to construct universal rate-adaptive LDPC codes are also investigated. 3. Error Floor of LDPC Codes: This project develops a rigorous framework to answer the following questions: Given an accepted level of the error floor, what is the best performance we can obtain? How can we achieve this performance?