Universal codeword sets and representations of the integers

By Peter Elias. 1975

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Citations in the corpus

cpSGD: Communication-efficient and differentially-private distributed SGD (2018, background): “, see [21] and in particular [5] showed that stochastic quantization and Elias coding [15] can be used to obtain communication-optimal SGD for convex functions.”
Distributed Mean Estimation with Limited Communication (2016, background): “. It can also provide lower quantization error in some scenarios due to better constants (see Section 7 for details). Concurrent to this work, [2] showed that stochastic quantization and Elias coding [11] can be used to obtain communication-optimal SGD. Recently, [16] showed that πsb can be improved”
Fisher information and stochastic complexity (1996, background): “Define the set I? = (2-u, a.), which plays the role of the interior of a compact set in Section 11. We selected these boundaries because they can be encoded with a short code length, in fact with about c + log* fi bits, where c is about 2.87 and log* x = log x + log log x + . . I, the dots indicatin”
Artemis: tight convergence guarantees for bidirectional compression in Federated Learning (2020, methodology): “To broadcast the quantized value, we use the Elias encoding [10].”
On the Convergence of Quantized Parallel Restarted SGD for Serverless Learning (2020, methodology): “Compression Schemes For any integer k, we use Elias gamma encoding [6], denoted as Elias(k), to generate its code.”
Compressed full-text indexes (2007, methodology): “An efficient way to compress the occurrence lists uses differential encoding plus a variable-length coding, such as Elias-δ coding [Elias 1975; Witten et al. 1999].”
Exploring single-sample SNP and INDEL calling with whole-genome de novo assembly (2012, methodology): “e used the established algorithm to merge BWTs of subsets of reads (Hon et al., 2007; Siren, 2009; Ferragina et al., 2010). The BWT string is run-length encoded with the length in the delta encoding (Elias, 1975). 2.7.2 Error correction Fermi corrects potential sequencing errors using an algorithm s”
A General SIMD-Based Approach to Accelerating Compression Algorithms (2015, methodology): “…is extended from the traditional Simple algorithms [Anh and Moffat 2005; Anh and Moffat 2006], which can be considered as a word-aligned algorithm; Group-Scheme extends Elias Gamma coding [Elias 1975], which can be considered as a family containing both bit-aligned and byte-aligned variants.”
Efficient storage of high throughput DNA sequencing data using reference-based compression. (2011, background): “Deletion lengths are currently Gamma encoded (Elias 1975).”
Decoding billions of integers per second through vectorization (2012, methodology): “An Elias gamma code [29, 30, 33] consists of two parts.”
SILT: a memory-efficient, high-performance key-value store (2011, methodology): “When | L | is small enough (e.g., ≤ 16), SortedStore uses static, glob-# 2 ) using Elias gamma coding [23] to avoid ﬁlling the CPU cache with large Huffman tables.”
Succinct nearest neighbor search (2011, methodology): “Each difference is encoded using Elias-γ [8] which is a variable-length integer encoding using 2 log x + 1 bits to encode an integer x.”