Lower Bounds on the Redundancy of Huffman Codes With Known and Unknown Probabilities

Blanes, Ian; Hernández-Cabronero, Miguel; Serra-Sagristà, Joan; Marcellin, Michael W.

doi:10.1109/access.2019.2932206

Cited by 5 publications

(4 citation statements)

References 35 publications

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“…Note that the oscillatory nature of all performance curves is related to the intrinsic ability of variable-to-fixed codes to efficiently represent some symbol probability distributions. The interested reader is referred to [58], [59] for a more complete explanation to this behavior.…”

Section: ) Code Forest Efficiencymentioning

confidence: 97%

High-Throughput Variable-to-Fixed Entropy Codec Using Selective, Stochastic Code Forests

et al. 2020

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Efficient high-throughput (HT) compression algorithms are paramount to meet the stringent constraints of present and upcoming data storage, processing, and transmission systems. In particular, latency, bandwidth and energy requirements are critical for those systems. Most HT codecs are designed to maximize compression speed, and secondarily to minimize compressed lengths. On the other hand, decompression speed is often equally or more critical than compression speed, especially in scenarios where decompression is performed multiple times and/or at critical parts of a system. In this work, an algorithm to design variable-to-fixed (VF) codes is proposed that prioritizes decompression speed. Stationary Markov analysis is employed to generate multiple, jointly optimized codes (denoted code forests). Their average compression efficiency is on par with the state of the art in VF codes, e.g., within 1% of Yamamoto et al.'s algorithm. The proposed code forest structure enables the implementation of highly efficient codecs, with decompression speeds 3.8 times faster than other state-of-the-art HT entropy codecs with equal or better compression ratios for natural data sources. Compared to these HT codecs, the proposed forests yields similar compression efficiency and speeds. INDEX TERMS Data compression, high-throughput entropy coding, variable-to-fixed codes.

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Section: ) Code Forest Efficiencymentioning

confidence: 97%

High-Throughput Variable-to-Fixed Entropy Codec Using Selective, Stochastic Code Forests

et al. 2020

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“…The symbols generated by dual-quant present a centralized and symmetric distribution, as shown in Figure 5. The generated codewords are highly related to the distribution of symbol frequencies [3]. These good characteristics inspire us to evaluate the similarity of two sets of symbol frequencies using STD.…”

Section: Adaptive Online Codewords Updatesmentioning

confidence: 99%

“…I/O and communication costs can quickly overwhelm the overall performance as parallel computers grow towards exascale. For instance, a well-known cosmological simulation code Nyx [2] can generate up to 2.8 TB of data for a single snapshot under a simulation resolution of 4096 3 , requiring to save a total of 2.8 PB data, when running the simulation for 5 times with 200 snapshots dumped per run.…”

Section: Introductionmentioning

confidence: 99%

Ceaz

Zhang

Jin

Geng

et al. 2022

Proceedings of the 36th ACM International Conference on Supercomputing

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As HPC systems continue to grow to exascale, the amount of data that needs to be saved or transmitted is exploding. To this end, many previous works have studied using error-bounded lossy compressors to reduce the data size and improve the I/O performance. However, little work has been done for effectively offloading lossy compression onto FPGA-based SmartNICs to reduce the compression overhead. In this paper, we propose a hardware-algorithm codesign for an efficient and adaptive lossy compressor for scientific data on FPGAs (called CEAZ), which is the first lossy compressor that can achieve high compression ratios and throughputs simultaneously. Specifically, we propose an efficient Huffman coding approach that can adaptively update Huffman codewords online based on codewords generated offline, from a variety of representative scientific datasets. Moreover, we derive a theoretical analysis to support a precise control of compression ratio under an errorbounded compression mode, enabling accurate offline Huffman codewords generation. This also helps us create a fixed-ratio compression mode for consistent throughput. In addition, we develop an efficient compression pipeline by adopting cuSZ's dual-quantization algorithm to our hardware use cases. Finally, we evaluate CEAZ on five real-world datasets with both a single FPGA board and 128 nodes (to accelerate parallel I/O). Experiments show that CEAZ outperforms the second-best FPGA-based lossy compressor by 2.3× of throughput and 3.0× of ratio. It also improves MPI_File_write and MPI_Gather throughputs by up to 28.9× and 37.8×, respectively. CCS CONCEPTS• Computer systems organization → Reconfigurable computing.

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“…There are several books in computer sciences that discuss its various applications in great detail [28]- [30]. Additionally, many articles (e.g., [36], [37], [46], [47]) appeared that use the probability bounds to address some of the algorithmic issues, such as decision analysis problems and structural engineering design decisions.…”

Section: Introductionmentioning

confidence: 99%

New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols

Hafid

Samih

2019

IEEE Access

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In recent years, the scalability issue of blockchain protocols has received huge attention. Sharding is one of the most promising solutions to scale blockchain. The basic idea behind sharding is to divide the blockchain network into multiple committees where each committee processes a separate set of transactions. In this paper, we propose a mathematical model to analyze the security of sharding-based blockchain protocols. Moreover, we analyze well-known sharding protocols including RapidChain, OmniLedger, and Zilliga to validate our model. The key contribution of our paper is to bound the failure probability for one committee and so for each epoch using probability bounds for sums of upper-bounded hypergeometric and binomial distributions. In addition, this paper contribution answers the following fundamental question: ''how to keep the failure probability, for a given sharding protocol, smaller than a predefined threshold?''. Three probability bounds are used: Chebyshev, Hoeffding, and Chvátal. To illustrate the effectiveness of our proposed model, we conduct a numerical and comparative analysis of the proposed bounds.

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Lower Bounds on the Redundancy of Huffman Codes With Known and Unknown Probabilities

Cited by 5 publications

References 35 publications

High-Throughput Variable-to-Fixed Entropy Codec Using Selective, Stochastic Code Forests

High-Throughput Variable-to-Fixed Entropy Codec Using Selective, Stochastic Code Forests

Ceaz

New Mathematical Model to Analyze Security of Sharding-Based Blockchain Protocols

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