Variable-length Prefix Codes with Multiple Delimiters

Anisimov, A. V.; Zavadskyi, Igor O.

doi:10.1109/tit.2017.2674670

Cited by 12 publications

(10 citation statements)

References 25 publications

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“…While there exist several modern compression techniques [3][4][5]37], each with different strengths and trade-offs, we compare a multidimensional Fibonacci code with the classical one, using the well-established Huffman code as a benchmark.…”

Section: Compression Efficiency and Simulation Resultsmentioning

confidence: 99%

“…Popular alternatives to these codes are codes with suffix delimiters, where certain patterns mark the end of a codeword [5]. A competent example in this class of codes is the Fibonacci code, which is a result of a binary numeration system for the integers known as Zeckendorf representation.…”

Section: Introductionmentioning

confidence: 99%

“…While suffix codes have been shown to offer adjustability to some extent [5], a great burden for a code with suffix delimiters to bear is its own suffix. A longer suffix gives more flexibility in the coded data, hence yielding denser codes, but obviously the codewords now have to carry longer appendage.…”

Section: Introductionmentioning

confidence: 99%

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Multidimensional Fibonacci Coding

2022

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Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci sequence increases but at the price of the increased suffix length. We propose a circumvention to this problem by introducing higher-dimensional Fibonacci codes for integer vectors. The resulting multidimensional Fibonacci coding is comparable to the classical one in terms of compression; while encoding several numbers all at once for a shared suffix generally results in a shorter codeword, the efficiency takes a backlash when terms from different orders of magnitude are encoded together. In addition, while laying the groundwork for the new encoding scheme, we provide extensive theoretical background and generalize the theorem of Zeckendorf to higher order. As such, our work unifies several variations of Zeckendorf’s theorem while also providing new grounds for its legitimacy.

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Section: Compression Efficiency and Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multidimensional Fibonacci Coding

2022

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“…The Fibonacci code is the special case π = 11. A more recent example can be found in [24], which extends the set of codewords by allowing multiple delimiters. As the authors report better compression performance than for the Fibonacci codes, one may also expect an improvement for the corresponding rewriting codes.…”

Section: Discussionmentioning

confidence: 99%

Context Sensitive Rewriting Codes for Flash Memory†

Klein

Shapira

2018

The Computer Journal

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Writing data on flash memory is asymmetric in the sense that it is possible to change a 0 into a 1-bit, but erasing a 1 back to value 0 is much more expensive and can only be done in blocks. This has triggered the development of rewriting codes in which new data can overwrite the old one, subject to the constraint of never changing a 1 into a zero. The notion of context-sensitive rewriting codes is introduced and we bring here the analysis of the compression performance of a family of such codes, based on generalizations of the Fibonacci sequence. This is then compared with experimental results.

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“…Any reverse multi-delimiter code R m 1 ,...,mt contains the same number of codewords of a given length as the "direct" multi-delimiter code D m 1 ,...,mt discussed in [13]. Thus, reverse MD-codes possess all properties of MD-codes such as completeness and universality as well as their asymptotic densities.…”

Section: Definitionmentioning

confidence: 99%

Efficient Integer Retrieving from Unordered Compressed Sequences

Zavadskyi

2023

Preprint

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We investigate the problem of fast direct access to elements of an integer sequence given in a compressed form. If integers are sorted in ascending order, it can be reduced to performing the 'select' operation on a bitmap, which is very well investigated. We focus on more general and more complicated case of unordered integer sequence and propose to represent it with the help of variable-length Reverse Multi-Delimiter (RMD) codes. When applied to data compression, these codes combine a good compression ratio with fast decoding. In this paper, another property of RMD-codes is researched - the ability of direct access to codewords in the encoded bitstream. We present the method allowing us to extract and decode a codeword from an RMD-bitstream in almost constant time and make experiments on its application to natural language text compression. Due to properties of RMD-codes and compactness of auxiliary direct access structures our method appears to be very space efficient requiring only a few percent excess over the entropy.

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Variable-length Prefix Codes with Multiple Delimiters

Cited by 12 publications

References 25 publications

Multidimensional Fibonacci Coding

Multidimensional Fibonacci Coding

Context Sensitive Rewriting Codes for Flash Memory†

Efficient Integer Retrieving from Unordered Compressed Sequences

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