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.
