Low Density Parity Check Coding: Applications and New Challenges

大量用于计算和电信的联网设备的快速发展为编码提出了具有挑战性和激动人心的新问题。通信系统设计者总是要在可靠性、可用带宽的有效利用、数据吞吐量和成本之间进行权衡。纠错编码是解决这些权衡问题的最强大的工具之一。在纠错方面稍有改进，就可以大大节省系统的总成本。低密度奇偶校验(LDPC)码有望成为编码专家提出的问题的最终答案。虽然人们对LDPC码进行了大量的研究，但研究人员认为，LDPC码在解决许多实际相关的编码问题方面的潜力尚未被发现，例如码率兼容编码、改进的译码和用于错误检测的编码。今天，对可靠传输或存储数据的速率的理论限制是众所周知的，因为许多电信挑战。今天和明天的挑战是在网络、分布式计算和通信应用中使用LDPC码。本文首先研究了MBIOS信道上的有限长度和无限长度删余LDPC码。给出了删余LDPC系综性能随删余分数变化的下界。利用这一点，研究人员计划得出良好的穿孔模式和程度分布的标准。然后，研究了改进的译码算法，该算法在MBIOS信道上的性能比标准迭代译码高出一个数量级。其目的是推导出用于改进的解码以成功完成解码的猜测比特和界的选择条件(关于猜测比特和界的数目)。最后，研究了LDPC码的检错能力，并分析了计算复杂度和集成平均性能之间的权衡。

The rapid development of a myriad of networked devices for computing and telecommunications presents challenging and exciting new issues for coding. Communication system designers always have to deal with trade-offs among reliability, efficient use of available bandwidth, data throughput and cost. Error-correction coding is one of the most powerful tools available to address these trade-offs. A small improvement in error-correction can yield large savings in the overall cost of systems. Low-Density Parity-Check (LDPC) codes promise to be the ultimate answer to the questions of coding specialists. Although a great amount of research has gone into LDPC codes, the investigators believe that the potency of LDPC codes in resolving many practically relevant coding issues such as rate-compatible coding, improved decoding and coding for error detection has yet to be discovered. Today, theoretical limits on rates at which reliable transmission or storage of data is possible are known for manytelecommunications challenges. Today's and tomorrow's challenges are to employ LDPC codes in networked, distributed computing and communications applications. This work first investigates finite and infinite length punctured LDPC codes over MBIOS channels. Bounds on the performance degradation of punctured LDPC ensembles as a function of puncturing fraction are derived. Using which, the investigators plan to arrive at criteria for good puncturing patterns and degree distributions. Then, the research expands on improved decoding algorithms thatoutperform standard iterative decoding by orders of magnitude over MBIOS channels. The intention is to derive conditions on the choice of guessed bits and bounds (on the number of them) for the improved decoding to successfully complete decoding. Finally, the research investigates the error detection capability of LDPC codes and analyzes the tradeoff between computational complexity and average performance of ensembles.