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020 _a9783319531397
_9978-3-319-53139-7
024 7 _a10.1007/978-3-319-53139-7
_2doi
050 4 _aQA297.4
072 7 _aPBD
_2bicssc
072 7 _aMAT036000
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072 7 _aPBD
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082 0 4 _a511.1
_223
100 1 _aAhlswede, Rudolf.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_959446
245 1 0 _aCombinatorial Methods and Models
_h[electronic resource] :
_bRudolf Ahlswede’s Lectures on Information Theory 4 /
_cby Rudolf Ahlswede ; edited by Alexander Ahlswede, Ingo Althöfer, Christian Deppe, Ulrich Tamm.
250 _a1st ed. 2018.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
300 _aXVIII, 385 p. 11 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
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490 1 _aFoundations in Signal Processing, Communications and Networking,
_x1863-8546 ;
_v13
505 0 _aPreface -- I Combinatorial Methods for Information Theory. - II Combinatorial Models in Information Theory. - III Supplement -- Gedenkworte für Rudolf Ahlswede -- Commemorating Rudolf Ahlswede -- Comments by Alon Orlitzky -- Index.
520 _aThe fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede’s favourite research fields -- extremal problems in Combinatorics -- are presented. Whereas the first part of the book concentrates on combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.
650 0 _aDiscrete mathematics.
_912873
650 0 _aComputer science—Mathematics.
_931682
650 1 4 _aDiscrete Mathematics.
_912873
650 2 4 _aMathematical Applications in Computer Science.
_931683
700 1 _aAhlswede, Alexander.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_959447
700 1 _aAlthöfer, Ingo.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_959448
700 1 _aDeppe, Christian.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_959449
700 1 _aTamm, Ulrich.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_959450
710 2 _aSpringerLink (Online service)
_959451
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319531373
776 0 8 _iPrinted edition:
_z9783319531380
776 0 8 _iPrinted edition:
_z9783319850733
830 0 _aFoundations in Signal Processing, Communications and Networking,
_x1863-8546 ;
_v13
_959452
856 4 0 _uhttps://doi.org/10.1007/978-3-319-53139-7
912 _aZDB-2-ENG
912 _aZDB-2-SXE
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