Tunstall Code, Khodak Variations, and Random Walks

Drmota, Michael; Reznik, Yuriy A.; Szpankowski, Wojciech

doi:10.1109/tit.2010.2046248

Cited by 22 publications

(20 citation statements)

References 30 publications

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“…For example, in [19] an error resilient Lempel-Ziv'77 scheme has been designed that also can be used for information hiding. In [23] and [33] we propose a precise analysis of variable-to-variable code that achieves very small redundancy. This was thoroughly discussed in our invited paper [28].…”

Section: Summary Of Technical Resultsmentioning

confidence: 99%

Information Transfer Ion Wireless Networks

Konorski¹

2010

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)22-07-2010 REPORT TYPE Final Report DATES COVERED (From -To) PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Gdansk University of Technology ul. Narutowicza 11/12 Gdansk 80-952 Poland PERFORMING ORGANIZATION REPORT NUMBERN/A SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)EOARD Unit 4515 BOX 14 APO AE 09421 SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S)Grant 08-3018 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTAd hoc, mesh, and other unstructured wireless networks are worth studying due to their potential of becoming an alternative, survivable communication infrastructure in case of a major disaster or security breach incapacitating the wired backbone. While the design of effective data transfer mechanisms in wireless networks is maturing, new challenges arise regarding information transfer. This is partly because wireless nodes' increased autonomy and anonymity lead to non-punishable node selfishness. Hence, relative to wired networks, it is no longer clear if a given piece of protocol data carries information -i.e., if it increases a selfish recipient's ability to achieve its objectives. Thus the distinction between data and information is linked to incentive compatibility and nodes' willingness to contribute to the network functionality. At the same time, measuring the amount of information in transferred data becomes vital. Accordingly, the project focused both on game-theoretic and information-theoretic aspects of wireless networks. SUBJECT TERMS

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Section: Summary Of Technical Resultsmentioning

confidence: 99%

Information Transfer Ion Wireless Networks

Konorski¹

2010

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“…It is known that every Khodak code is a Tunstall code, and that for the same dictionary size, the Khodak code has asymptotically the same average phrase length as the Tunstall code [20]. We show: THEOREM 3.2.…”

Section: Rlementioning

confidence: 86%

“…, 2 −1 , the corresponding graph contains the non-leaf vertices (0, i) and (i, 0), and the leaf vertices (1, i) and Khodak Code. The Khodak code [20] is is obtained by modifying…”

Section: Rlementioning

confidence: 99%

See 1 more Smart Citation

Compressed Bit Vectors Based on Variable-to-Fixed Encodings

Jo¹,

Joannou²,

Okanohara³

et al. 2014

2014 Data Compression Conference

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We consider practical implementations of compressed bitvectors, which support rank and select operations on a given bit-string, while storing the bit-string in compressed form. Our approach relies on variable-to-fixed encodings of the bit-string, an approach that has not yet been considered systematically for practical encodings of bitvectors. We show that this approach leads to fast practical implementations with low redundancy (i.e., the space used by the bitvector in addition to the compressed representation of the bit-string), and is a flexible and promising solution to the problem of supporting rank and select on moderately compressible bit-strings, such as those encountered in real-world applications.

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“…There are several well known variable-tofixed algorithms; e.g., Tunstall and Khodak schemes (cf. [10], [17], [25]). Boncelet's algorithm is based on a divide and conquer strategy, and therefore is fast and easy to implement.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Block Arithmetic Coding: Discrete divide and conquer recurrences

Drmota

Szpankowski

2011

2011 IEEE International Symposium on Information Theory Proceedings

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In 1993 Boncelet introduced a block arithmetic scheme for entropy coding that combines advantages of stream arithmetic coding with algorithmic simplicity. It is a variableto-fixed length encoding in which the source sequence is partitioned into variable length phrases that are encoded by a fixed length dictionary pointer. The parsing is accomplished through a complete parsing tree whose leaves represent phrases. This tree, in its suboptimal heuristic version, is constructed by a simple divide and conquer algorithm, whose analysis is the subject of this paper. For a memoryless source, we first derive the average redundancy and compare it to the (asymptotically) optimal Tunstall's algorithm. Then we prove a central limit theorem for the phrase length. To establish these results, we apply powerful techniques such as Dirichlet series, Mellin-Perron formula, and (extended) Tauberian theorems of Wiener-Ikehara.

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Tunstall Code, Khodak Variations, and Random Walks

Cited by 22 publications

References 30 publications

Information Transfer Ion Wireless Networks

Information Transfer Ion Wireless Networks

Compressed Bit Vectors Based on Variable-to-Fixed Encodings

Analysis of a Block Arithmetic Coding: Discrete divide and conquer recurrences

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