Dynamic Shannon coding

Gagie, Travis

doi:10.1016/j.ipl.2006.09.015

Cited by 11 publications

(26 citation statements)

References 32 publications

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“…However, as opposed to the adaptive list-based structures that have been reported in the literature (for example, in block sorting [1] and in [2]) we argue that adaptive tree-based schemes have their distinct advantages, and this claim has been demonstrated by using the principles on a Fano scheme, which has recently attracted fascinating research attention [3,4].…”

Section: Introductionmentioning

confidence: 69%

“…This approach performs poorly machine word. Observe that in [3] Gagie introduced a new data structure to maintain a code-tree explicitly-which is also the spirit of our present work. † †…”

Section: Adaptive Lists and Treesmentioning

confidence: 99%

“…Consider the source alphabet S = {a, b, c, d, e} whose frequency counters are P = [8,3,3,3,3], and the code alphabet A = {0, 1}. A PBST, T = {t 1 , .…”

Section: Examplementioning

confidence: 99%

“…For any FBST, T, is calculated using (3). By optimizing on the relative properties of and , we can show that the average code word length of the encoding schemes generated from T,¯ , can be calculated from the values of and that are maintained at the root.…”

Section: Lemmamentioning

confidence: 99%

“…Figure 3. A PBST, T, constructed from S ={a, b, c, d, e, f, g} and P = [8,3,3,3,3,3,3], and the corresponding PBST, T , after performing an STL-3 operation. The dotted line above the top-most node indicates that this node could be a left child or a right child of its parent or could be the root node itself.…”

Section: Lemma 2 (Stl-1 Validity)mentioning

confidence: 99%

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An efficient compression scheme for data communication which uses a new family of self‐organizing binary search trees

Rueda

Oommen

2008

Int J Communication

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SUMMARYIn this paper, we demonstrate that we can effectively use the results from the field of adaptive selforganizing data structures in enhancing compression schemes. Unlike adaptive lists, which have already been used in compression, to the best of our knowledge, adaptive self-organizing trees have not been used in this regard. To achieve this, we introduce a new data structure, the partitioning binary search tree (PBST) which, although based on the well-known binary search tree (BST), also appropriately partitions the data elements into mutually exclusive sets. When used in conjunction with Fano encoding, the PBST leads to the so-called Fano binary search tree (FBST), which, indeed, incorporates the required Fano coding (nearly equal probability) property into the BST. We demonstrate how both the PBST and the FBST can be maintained adaptively and in a self-organizing manner. The updating procedure that converts a PBST into an FBST, and the corresponding new tree-based operators, namely the shift-to-left and the shift-to-right operators, are explicitly presented. The encoding and decoding procedures that also update the FBST have been implemented and rigorously tested. Our empirical results on the files of the well-known benchmarks, the Calgary and Canterbury Corpora, show that the adaptive Fano coding using FBSTs, the Huffman, and the greedy adaptive Fano coding achieve similar compression ratios. However, in terms of encoding/decoding speed, the new scheme is much faster than the latter two in the encoding phase, and they achieve approximately the same speed in the decoding phase. We believe that the same philosophy, namely that of using an adaptive self-organizing BST to maintain the frequencies, can also be utilized for other data encoding mechanisms, even as the Fenwick scheme has been used in arithmetic coding.

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Section: Introductionmentioning

confidence: 69%

Section: Adaptive Lists and Treesmentioning

confidence: 99%

“…Consider the source alphabet S = {a, b, c, d, e} whose frequency counters are P = [8,3,3,3,3], and the code alphabet A = {0, 1}. A PBST, T = {t 1 , .…”

Section: Examplementioning

confidence: 99%

Section: Lemmamentioning

confidence: 99%

Section: Lemma 2 (Stl-1 Validity)mentioning

confidence: 99%

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An efficient compression scheme for data communication which uses a new family of self‐organizing binary search trees

Rueda

Oommen

2008

Int J Communication

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Yang

Jin

et al. 2008

Int J Communication

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Worst-Case Optimal Adaptive Prefix Coding

Gagie

Nekrich

2009

Lecture Notes in Computer Science

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Abstract.A common complaint about adaptive prefix coding is that it is much slower than static prefix coding. Karpinski and Nekrich recently took an important step towards resolving this: they gave an adaptive Shannon coding algorithm that encodes each character in O(1) amortized time and decodes it in O(log H) amortized time, where H is the empirical entropy of the input string s. For comparison, Gagie's adaptive Shannon coder and both Knuth's and Vitter's adaptive Huffman coders all use Θ(H) amortized time for each character. In this paper we give an adaptive Shannon coder that both encodes and decodes each character in O(1) worst-case time. As with both previous adaptive Shannon coders, we store s in at most (H + 1)|s| + o(|s|) bits. We also show that this encoding length is worst-case optimal up to the lower order term.

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Dynamic Shannon coding

Cited by 11 publications

References 32 publications

An efficient compression scheme for data communication which uses a new family of self‐organizing binary search trees

An efficient compression scheme for data communication which uses a new family of self‐organizing binary search trees

Untitled

Worst-Case Optimal Adaptive Prefix Coding

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