Collaborative Research: Towards a Unified Framework for Decoding Algorithms: Unveiling the Hidden Connections

设计高效、低复杂度的编解码算法是无线和有线网络优化的关键。近年来，出现了新的强大的范例，例如，信念传播，以及经典方法的复兴，例如，顺序译码，用于译码算法的设计。本研究的主要目标是在一个框架下统一一类利用局部约束的算法，例如，线性规划或置信传播解码器及其推广，具有优化全局代价函数的一类算法，例如，树搜索解码器。拟议的研究受益于我们的初步结果，建立了不同解码方案之间有趣的联系（如续集中详细介绍的）。我们的研究结果有望阐明已知算法的特性，并启发设计更强大的解码器。我们的研究将从传统的点对点场景开始，其中模型的复杂性范围从简化的二进制擦除信道到具有挑战性的多径衰落信道。在后一种情况下，我们的工作将针对联合检测和解码方法，并明确考虑相关的信号处理任务，例如，预处理阶段，这将在后续严格定义。我们的研究将继续调查三个不同类别的多用户信道。第一个推力将集中在中断有限的多址信道，高效的解码算法，实现最佳的分集复用权衡将被追求。同样的工作路线也将寻求实现复合多址信道（CMAC）容量的代码集合和解码算法，这是著名的连续消除解码器未能实现容量的少数例子之一。CMAC模型捕捉的基本特性的延迟有限的多址信道与有限的发射机信道状态信息。广播频道的研究（即，下行链路）是我们的第二个研究重点，其中低复杂度和高性能的脏纸码和无比率码将被构造。在此背景下，经典的工作树搜索源codingwill被重新审视，以构建低复杂度的矢量量化阶段的dirty-paper codingscheme。第三个研究重点是合作渠道。在这里，我们的努力将寻求表征分集复用的协同干扰信道的权衡与相关的最佳编码和解码算法沿着。这项工作将建立在CMAC和干扰信道之间的密切关系。最后，受我们最近在该领域工作的启发，我们将推出新的合作格编码和解码算法，所提出的研究的智力价值在于所提出的问题的基本性质和预期的信息和编码理论的贡献。本课程将在信息论与最优化和代数数论之间建立新的桥梁。此外，还将研究有助于解码算法设计和分析的分析工具和有效的数值方法。具有信息论、编码理论、无线通信和信号处理方面集体专长的PI，组建一个合格的团队来承担研究计划。该项目建立在PI正在进行的合作的最新成果之上。本文的理论研究将对信息论和信号处理领域产生广泛的影响。此外，预期的结果将有助于设计有效的编码/解码算法，渗透到许多应用程序（请参阅德州仪器和ST微电子的支持信）。在教育方面，两所参与机构的研究生将积极参与研究活动。

The design of efficient, and low complexity, coding and decoding algorithms is a critical component inthe optimization of wireless and wire-line networks. Recent years have witnessed the emergence of newpowerful paradigms, e.g., belief propagation, as well as the revival of classical approaches, e.g., sequentialdecoding, for the design of decoding algorithms. This proposal seeks a deeper theoretical foundation for thedesign and analysis of efficient decoding algorithms, along with the associated code ensembles, by buildingon this recent progress.The overarching goal of the proposed research is to unify under one framework the class of algorithmsthat exploit the power of local constraints, e.g., the linear programming or belief propagation decoders andgeneralization thereof, with the class of algorithms that optimize a global cost function, e.g., tree searchdecoders. The proposed research benefits from our preliminary results that establish interesting connectionsbetween different decoding schemes (as detailed in the sequel). Our results are expected to elucidate theproperties of known algorithms and inspire the design of more powerful decoders. Our investigationswill start with the traditional point-to-point scenario where the complexity of the model ranges from thesimplified binary erasure channel to the challenging multi-path fading channel. In the latter case, ourwork will target a joint detection and decoding approach and consider, explicitly, the associated signalprocessing tasks, e.g., the preprocessing stage which will be defined rigorously in the sequel.Our research will then proceed to investigate three distinct categories of multi-user channels. Thefirst thrust will focus on the outage-limited multiple access channel where efficient decoding algorithmsthat achieve the optimal diversity-multiplexing tradeoff will be pursued. The same line of work will alsoseek code ensembles and decoding algorithms that achieve the capacity of the compound multiple accesschannel (CMAC), one of the few examples where the celebrated successive cancellation decoder fails toachieve capacity. The CMAC model captures the essential characteristics of delay-limited multiple accesschannels with limited transmitter channel state information. The study of the broadcast channel (i.e.,downlink) is our second research thrust where low complexity and high performance dirty paper codesand rateless codes will be constructed. Within this context, classical works on tree search source codingwill be revisited in order to construct low complexity vector quantization stage for the dirty-paper codingscheme. The third research thrust will be devoted to cooperative channels. Here, our efforts will seekto characterize the diversity-multiplexing tradeoff of the cooperative interference channel along with theassociated optimal coding and decoding algorithms. This work will build on the intimate relationshipbetween the CMAC and the interference channel. Finally, inspired by our recent work in the area, novelapproaches for cooperative lattice coding and decoding algorithms will be unveiled.The intellectual merit of the proposed research lies in the fundamental nature of the posed questionsand the expected contributions to information and coding theories. New bridges between informationtheory, from one side, and optimization and algebraic number theories, from the other side, will be built.Furthermore, analytical tools, as well as efficient numerical methods, that aid in the design and analysisof decoding algorithms will be pursued.The PIs, with collective expertise in information theory, coding theory, wireless communications, andsignal processing, form a qualified team for undertaking the research plan. This project builds on recentresults from the PIs' ongoing collaboration. The proposed theoretical research is expected to have a broadimpact on the information theory and signal processing communities. Furthermore, the anticipated resultswill contribute to the design of efficient encoding/decoding algorithms which percolate through manyapplications (please refer to the support letters from Texas Instruments and ST Microelectronics). On theeducational front, graduate students at the two participating institutions will be heavily involved in theresearch activities.