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Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST-equivariant) CNN with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve equivariance for the regular representation of the scaling-translation group ST. To reduce the model complexity and computational burden, we decompose the convolutional filters under two pre-fixed separable bases and truncate the expansion to low-frequency components. A further benefit of the truncated filtermore »Free, publicly-accessible full text available April 1, 2023
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Encoding the scale information explicitly into the representation learned by a convolutional neural network (CNN) is beneficial for many computer vision tasks especially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST-equivariant) CNN with joint convolutions across the space and the scaling group, which is shown to be both sufficient and necessary to achieve equivariance for the regular representation of the scaling-translation group ST. To reduce the model complexity and computational burden, we decompose the convolutional filters under two pre-fixed separable bases and truncate the expansion to low-frequency components. A further benefit of the truncated filtermore »Free, publicly-accessible full text available April 1, 2023
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Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal processing that reduce the effect of physical instabilities. Constrained codes are used in storage to avoid problematic patterns. Recently, we introduced binary symmetric lexicographically-ordered constrained codes (LOCO codes) for data storage and transmission. This paper introduces simple constrained codes that support non-binary physical gates in multi, triple, quad, and the currently-in-development penta-level cell (M/T/Q/P-LC) Flash memories. The new codes can be easily modified ifmore »
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Racetrack memory is a promising new non-volatile memory technology, especially because of the density of its 3D implementation. However, for 3D racetrack to reach its potential, certain reliability issues must be overcome. Prior work used per-track encoding to tolerate the shift errors that are unique to racetrack, but no solutions existed for tolerating both shift errors and bit flip errors. We introduce Foosball Coding, which combines per-track coding for shift errors with a novel across-track coding for bit flips. Moreover, our per-track coding scheme methodically explores the design of inter-codeword delimiters and introduces the novel concept of multi-purpose delimiters, inmore »
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The continuous rise of the blockchain technology is moving various information systems towards decentralization. Blockchain-based decentralized storage networks (DSNs) offer significantly higher privacy and lower costs to customers compared with centralized cloud storage associated with specific vendors. Coding is required to retrieve data stored on failing components. While coding solutions for centralized storage have been intensely studied, those for DSNs have not yet been discussed. In this paper, we propose a coding scheme where each node receives extra protection through cooperation with nodes in its neighborhood in a heterogeneous DSN with any given topology. Our scheme can achieve faster recoverymore »
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Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical T and T † gates. For example, this could enable magic state distillation with non-CSS codes and, thus, provide better parameters than CSS-based protocols. However, among non-degenerate stabilizer codes that support transversal T, we prove that CSS codes are optimal. We also show that triorthogonal codes are, essentially, the only family of CSS codes that realize logical transversal T via physical transversal T. Using our algebraic approach, we reveal new purely-classical coding problems thatmore »