Low Density Parity Check Coding: Applications and New Challenges

用于计算和电信的无数联网设备的快速发展为编码提出了具有挑战性和令人兴奋的新问题。通信系统的设计者总是必须在可靠性、有效利用可用带宽、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的最强大的工具之一。纠错方面的一个小的改进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问题的最终答案。尽管对LDPC码的研究已经很多，但研究者认为LDPC码在解决诸如速率兼容编码、改进的解码和用于错误检测的编码等许多实际相关的编码问题方面的潜力还有待于发现。今天，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信道上的有限和无限长删余LDPC码。 导出了删余LDPC码系综性能下降的界，它是删余分数的函数。使用它，研究人员计划达到良好的穿孔模式和度分布的标准。然后，研究了改进的译码算法，其性能在MBIOS信道上比标准迭代译码提高了几个数量级。其目的是推导出条件的猜测位和边界的选择（对他们的数量）的改进的解码，以成功地完成解码。最后，研究了LDPC码的检错性能，并分析了计算复杂度和系综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.