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

摘要：-NSF项目正在研究可用于译码低密度奇偶校验(LDPC)码的非传统模拟技术背后的理论基础。基于自下而上方法的优雅公式，正在开发新的模拟解码技术，其中使用设备物理中固有的计算原语来设计编码和解码算法。特别是，我们正在研究用于设计高性能LDPC码解码器的裕度传播原理。边缘传播原理(MPP)提供了一种有趣的模拟域物理工具，用于评估信息论度量(例如，熵)和其他量(例如，似然函数)，它只利用物理量(电流、电荷、质量、能量)的基本守恒定律进行计算，因此可以在微/纳米设备(硅、MEMS、微流体)上进行扩展。本研究集中在四个具体领域：(A)将边缘传播原理映射到图形化方法，并开发新的LDPC码译码算法；(B)对边缘传播设备中固有的噪声进行建模，并评估其对LDPC译码算法的影响；(C)开发基于密度进化的分析信道编码工具，以优化基于裕度传播的LDPC解码器的性能；(D)在硅片上实现裕度传播LDPC解码器的原型。这项研究的更广泛影响包括设计高性能低密度校验码解码器的新算法和硬件，这些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被用于设计新的教材，用于培训通信和电子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.