Investigation into Non-conventional Analog Decoders for Low-density Parity Check Codes

摘要：----------这个NSF项目正在研究可用于解码低密度奇偶校验（LDPC）码的非常规模拟技术背后的理论基础。新的模拟解码技术正在开发基于自下而上方法的优雅公式，其中设备物理中固有的计算原语用于设计编码和解码算法。特别是，我们正在研究余量传播原理，以设计LDPC码的高性能解码器。边际传播原理（MPP）提供了一个有趣的模拟域物理工具，用于评估信息论度量（例如，熵）和其他数量（例如，似然函数），仅利用物理量（电流，电荷，质量，能量）的基本守恒定律进行计算，因此可扩展到微/纳米器件（硅，MEMS，微流体）。本研究集中在四个具体领域：(a)将边界传播原理映射到图形方法并开发解码LDPC代码的新算法；(b)模拟边缘传播设备固有的噪声，并评估其对LDPC解码算法的影响；(c)开发基于密度演化的分析信道编码工具，优化基于余量传播的LDPC解码器的性能；(d)在硅中制作边缘传播LDPC解码器的原型。本研究的广泛影响包括设计高性能LDPC解码器的新算法和硬件，可用于当前和未来的数字通信标准（DVB-S2, 802.11, 802.12, 802.16, 802.20）。开发的算法和硬件正在用于设计新的教材，用于训练通信和电子学跨学科领域的研究生。

Abstract:----------This NSF project is investigating theoretical foundations behind non-conventional analog techniques that can be used for decoding low-density parity check (LDPC) codes. New analog decoding techniques are being developed based on elegant formulations of a bottom-up approach where computational primitives inherent in device physics are used for designing encoding and decoding algorithms. In particular, we are investigating margin propagation principles for designing high-performance decoders for LDPC codes. Margin propagation principle (MPP), which provides an intriguing analog-domain physical tool for evaluating information-theoretic measures (e.g., entropy) and other quantities (e.g., likelihood functions), utilizes only basic conservation laws of physical quantities (current, charge, mass, energy) for computing and therefore is scalable across micro/nano devices (silicon, MEMS, microfluidics).This research focuses on four specific areas: (a) mapping margin propagation principle to graphical methods and to develop novel algorithms for decoding LDPC codes; (b) modeling noise inherent in margin propagation devices and evaluating its impact on LDPC decoding algorithm; (c) developing analytical channel-coding tools based on density evolution for optimizing the performance of margin propagation based LDPC decoder; (d) prototyping a margin propagation LDPC decoder in silicon. The broader impact of this research includes novel algorithms and hardware for designing high-performance LDPC decoders, that can be used in present and future digital communication standards (DVB-S2, 802.11, 802.12, 802.16, 802.20). The developed algorithms and hardware are being utilized in the design of novel teaching materials, which are used to train graduate students in the interdisciplinary area of communications and electronics.