Low Density Parity Check Coding: Applications and New Challenges

计算和通信的无数网络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。通信系统设计者总是需要在可靠性、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。在纠错方面的一个小改进可以大大节省系统的总体成本。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码进行了大量的研究，但研究者认为LDPC码在解决许多实际相关的编码问题（如速率兼容编码、改进解码和错误检测编码）方面的效力尚未被发现。今天，对可靠传输或存储数据的速率的理论限制是许多电信挑战的已知原因。当前和未来的挑战是在网络、分布式计算和通信应用中使用LDPC代码。这项工作首先研究了MBIOS信道上有限长度和无限长度穿孔LDPC码。导出了被刺破LDPC系统性能退化随刺破分数的函数边界。利用这些数据，研究人员计划得出良好穿刺模式和度分布的标准。然后，研究扩展了改进的解码算法，在MBIOS信道上优于标准迭代解码的数量级。其目的是推导出选择猜测比特的条件和边界（它们的数量），以使改进的解码成功完成解码。最后，研究了LDPC码的错误检测能力，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.