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1. Efficient Nested Key Equation Solver for Short Generalized Integrated Interleaved BCH Codes

   Zhenshan Xie and Xinmiao Zhang (May 2022, Proceedings IEEE International Symposium on Circuits and Systems)

   Generalized integrated interleaved (GII) codes can nest BCH sub-codewords to form stronger BCH codewords. They are among the best candidates for error correction in the new storage class memories (SCMs). However, SCMs require short codeword length and low redundancy. In this case, the nested key equation solver (KES), which is a key step in GII decoding, has a small number of iterations. The initialization and/or scalar pre-computation in previous nested KES designs have large area and may take even longer time than the iterations themselves. This paper proposes an efficient nested KES design for short GII-BCH codes. The polynomial updating is decomposed into two steps to reduce the critical path without requiring scalar pre-computation. Besides, the KES is reformulated to reduce the number of clock cycles without incurring any area overhead. For an example code over GF(2^{10}) that protects 2560 bits with 10% redundancy, the proposed design achieves at least 25% area reduction and 37% reduction on the area-time product averaged over the nested decoding rounds compared to prior efforts. 

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2. An Efficient Parallel Architecture for Resource-Shareable Reed-Solomon Encoder

   https://doi.org/10.1109/SiPS52927.2021.00035  

   Tang, Yok Jye; Zhang, Xinmiao (October 2021, IEEE Workshop on Signal Processing Systems)

   Reed-Solomon (RS) codes are adopted in many digital communication and storage systems to ensure data reliability. For many of these systems, the encoder and decoder are not active at the same time. In previous designs, RS encoders implemented as linear feedback shift registers in a concatenated structure are reused to compute the syndromes so that the decoder complexity is reduced. However, the parallel versions of such encoders have very long critical path and hence can not achieve high speed. This paper proposes a new parallel resource-shareable RS encoder architecture based on the Chinese Remainder Theorem (CRT). The generator polynomial of RS codes is decomposed into factors of degree one and state transformation is developed to enable the sharing of the hardware units for syndrome computation. As a result, the critical path is reduced to only one multiplier and one adder, regardless of the parallelism. Additionally, by utilizing the property that the degrees of the decomposed polynomial factors are one, optimizations are also developed to greatly simplify the CRT-based encoder. For example encoders of a (255, 229) RS code over GF(2^8), our proposed design can achieve at least 29% higher efficiency in terms of area-time product for moderate or higher parallelisms compared to the previous resource-shareable RS encoder and traditional parallel RS encoders combined with syndrome computation units that implement the same functionality. 

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3. Exploring target function approximation for stochastic circuit minimization

   https://doi.org/10.1145/3400302.3415701  

   Wang, Chen; Xiao, Weihua; Hayes, John P.; Qian, Weikang (November 2020, ICCAD '20: Proceedings of the 39th International Conference on Computer-Aided Design)

   null (Ed.)

   Stochastic computing (SC) is an emerging paradigm for designing circuits to perform complicated computation with simple circuitry. Although SC circuits have small area and critical-path delay, due to the need of many clock cycles to perform computation, they have a large overall latency and energy consumption. One solution to this problem is to further minimize the circuits. In this work, we explore target function approximation to derive an SC circuit with significantly reduced area and delay. We propose two static methods that first construct a set of functions close to the given target function and then select the best synthesized SC circuit realizing one of these functions. We also propose an efficient dynamic method that simultaneously searches for the best approximated target function and the corresponding minimized SC circuit. The experimental results show that on average, our dynamic method dramatically reduces the area, critical-path delay, and area-delay product of the SC circuits by 80%, 59%, and 91%, respectively, over the state-of-the-art Maclaurin polynomial-based method for a given error bound of 2%. The code of our methods is made open-source. 

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4. Recycled ADMM: Improve Privacy and Accuracy with Less Computation in Distributed Algorithms

   Zhang, Xueru; Khalili, Mohammad Mahdi; Liu, Mingyan (January 2018, Annual Allerton Conference on Control, Communication, and Computing)

   Alternating direction method of multiplier (ADMM) is a powerful method to solve decentralized convex optimization problems. In distributed settings, each node performs computation with its local data and the local results are exchanged among neighboring nodes in an iterative fashion. During this iterative process the leakage of data privacy arises and can accumulate significantly over many iterations, making it difficult to balance the privacy-utility tradeoff. In this study we propose Recycled ADMM (R-ADMM), where a linear approximation is applied to every even iteration, its solution directly calculated using only results from the previous, odd iteration. It turns out that under such a scheme, half of the updates incur no privacy loss and require much less computation compared to the conventional ADMM. We obtain a sufficient condition for the convergence of R-ADMM and provide the privacy analysis based on objective perturbation. 

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5. Testing the limits of the global instability index

   https://doi.org/10.1063/5.0140480  

   Miller, Kyle_D; Rondinelli, James_M (October 2023, APL Materials)

   The global instability index (GII) is a computationally inexpensive bond valence-based metric originally designed to evaluate the total bond strain in a crystal. Recently, the GII has gained popularity as a feature of data-driven models in materials research. Although prior studies have proven that GII is an effective predictor of structural distortions and decomposition energy when applied to small datasets, the wider use of GII as a global indicator of structural stability has yet to be evaluated. To that end, we compute GII for thousands of compounds in inorganic structure databases and partition compounds by chemical interactions underlying their stability to understand the GII values and their variations. Our results show that the GII captures relative chemical trends, such as electronegativity, even beyond the intended domain of strongly ionic compounds. However, we also find that GII magnitudes vary significantly with factors such as chemistry (cation–anion identities and bond character), geometry (connectivity), data source, and model bias, making GII suitable for comparisons within controlled datasets but unsuitable as an absolute, universal metric for structural feasibility. 

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