We present two strategies to reduce the complexity of the alternating direction method of multipliers when applied to linear programming (ADMM-LP) decoding of low-density parity-check codes. First, to address the high complexity of computing a projection onto the parity polytope, the complexity bottleneck of ADMM-LP decoding, we propose the sparse affine projection algorithm (SAPA). SAPA projects onto the affine hull of χ ≤dnearby local codewords where the check degree isdand where χ can be significantly smaller thand. Unlike exact projection, SAPA does not require a water-filling process, and thus can be implemented with lower per-iteration complexity. Second, to reduce the number of effective iterations needed for ADMM-LP decoding, we propose a randomized layered scheduling framework. Rather than updating checks in round-robin fashion in each iteration, more “problematic” checks have a higher probability of being updated. The probability mass function that governs the selection of which checks to update is based upon the location of replica vectors inside (or on) the parity polytope. The resultant decoder converges significantly faster under this randomized scheduling than under round-robin scheduling. This makes it well suited for use in applications that limit the number of iterations.

A novel inductive electrostatic discharge (ESD) protection methodology for narrow-band (NB) and ultra-wideband (UWB) low noise amplifiers (LNA) is presented. Spectre post-layout simulations in a TSMC 0.18μm CMOS process show that the proposed primary-secondary inductive ESD protection can handle 4kV ESD stress. The proposed UWB LNA achieves a flat gain bandwidth of 2.7GHz to 9GHz, a power gain of 10dB, a minimum noise figure of 3.2dB and a total power dissipation of 6.6mW from a 1.2V supply.

Generation of digitally reconstructed radiographs (DRRs) is computationally expensive and is typically the rate-limiting step in the execution time of intensity-based two-dimensional to three-dimensional (2D-3D) registration algorithms. We address this computational issue by extending the technique of light field rendering from the computer graphics community. The extension of light fields, which we call attenuation fields (AFs), allows most of the DRR computation to be performed in a preprocessing step; after this precomputation step, DRRs can be generated substantially faster than with conventional ray casting. We derive expressions for the physical sizes of the two planes of an AF necessary to generate DRRs for a given X-ray camera geometry and all possible object motion within a specified range. Because an AF is a ray-based data structure, it is substantially more memory efficient than a huge table of precomputed DRRs because it eliminates the redundancy of replicated rays. Nonetheless, an AF can require substantial memory, which we address by compressing it using vector quantization. We compare DRRs generated using AFs (AF-DRRs) to those generated using ray casting (RC-DRRs) for a typical C-arm geometry and computed tomography images of several anatomic regions. They are quantitatively very similar: the median peak signal-to-noise ratio of AF-DRRs versus RC-DRRs is greater than 43 dB in all cases. We perform intensity-based 2D-3D registration using AF-DRRs and RC-DRRs and evaluate registration accuracy using gold-standard clinical spine image data from four patients. The registration accuracy and robustness of the two methods is virtually identical whereas the execution speed using AF-DRRs is an order of magnitude faster.