Decoding of block and convolutional codes in rank metric:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Shaker
2014
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| Schriftenreihe: | Berichte aus der Informationstechnik
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 136 S. graph. Darst. |
| ISBN: | 9783844026108 |
Internformat
MARC
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| 245 | 1 | 0 | |a Decoding of block and convolutional codes in rank metric |c Antonia Wachter-Zeh |
| 264 | 1 | |a Aachen |b Shaker |c 2014 | |
| 300 | |a XIV, 136 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
1 MOTIVATION AND OVERVIEW 1
2 INTRODUCTION TO CODES IN RANK METRIC 5
2.1 CODES OVER FINITE FIELDS 5
2.1.1 NOTATIONS FOR FINITE FIELDS 5
2.1.2 NORMAL BASES 7
2.1.3 BASICS OF BLOCK CODES AND DECODING PRINCIPLES 9
2.1.4 BASICS OF CONVOLUTIONAL CODES 13
2.2 LINEARIZED POLYNOMIALS 16
2.2.1 DEFINITION AND PROPERTIES 17
2.2.2 BASIC OPERATIONS 18
2.2.3 CONNECTION TO LINEAR MAPS 21
2.2.4 THE (INVERSE) (/-TRANSFORM 22
2.3 CODES IN RANK METRIC 23
2.3.1 RANK METRIC AND ITS PROPERTIES 24
2.3.2 GABIDULIN CODES 26
2.3.3 INTERLEAVED GABIDULIN CODES 29
2.3.4 LIFTED GABIDULIN CODES 31
3 DECODING APPROACHES FOR GABIDULIN CODES 33
3.1 FAST ALGORITHMS FOR LINEARIZED POLYNOMIALS 33
3.1.1 COMPLEXITY OF KNOWN APPROACHES AND OVERVIEW OF NEW APPROACHES 34
3.1.2 FAST LINEARIZED COMPOSITION USING FRAGMENTED POLYNOMIALS 37
3.1.3 FAST LINEARIZED COMPOSITION USING FAST MULTI-POINT EVALUATION 40
3.1.4 FAST LINEARIZED (EXTENDED) EUCLIDEAN ALGORITHM 43
3.2 DECODING OF GABIDULIN CODES 46
3.2.1 KNOWN SYNDROME-BASED DECODING APPROACHES 46
3.2.2 A GAO-LIKE DECODING ALGORITHM 52
3.2.3 ERROR-ERASURE DECODING 55
3.2.4 FAST ERROR-ERASURE DECODING OF ^-CYCLIC GABIDULIN CODES 59
3.3 SUMMARY AND OUTLOOK 61
4 DECODING APPROACHES FOR INTERLEAVED GABIDULIN CODES 63
4.1 KNOWN DECODING APPROACHES 63
4.2 PRINCIPLE OF INTERPOLATION-BASED DECODING 67
4.2.1 INTERPOLATION STEP 68
4.2.2 ROOT-FINDING STEP 70
4.3 INTERPOLATION-BASED DECODING APPROACHES 72
4.3.1 A LIST DECODING APPROACH 72
4.3.2 A PROBABILISTIC UNIQUE DECODING APPROACH 74
4.4 ERROR-ERASURE DECODING 77
4.5 SUMMARY AND OUTLOOK 79
IX
HTTP://D-NB.INFO/1047499665
CONTENTS
5 BOUNDS ON LIST DECODING OF BLOCK CODES IN RANK METRIC 81
5.1 KNOWN BOUNDS ON THE LIST SIZE FOR CODES IN HAMMING METRIC 82
5.2 CODES CONNECTED TO THE LIST OF DECODING AND PROBLEM STATEMENT 84
5.2.1 CONNECTION BETWEEN CONSTANT-DIMENSION AND CONSTANT-RANK CODES 84
5.2.2 PROBLEM STATEMENT 85
5.2.3 CONNECTION BETWEEN CONSTANT-RANK CODES AND THE LIST OF DECODING 86
5.3 A LOWER BOUND ON THE LIST SIZE FOR GABIDULIN CODES 87
5.4 AN UPPER BOUND ON THE LIST SIZE FOR RANK-METRIC CODES 89
5.5 A LOWER BOUND ON THE LIST SIZE FOR RANK-METRIC CODES 90
5.6 SUMMARY, COMPARISON TO HAMMING METRIC AND OUTLOOK 94
6 CONVOLUTIONAL CODES IN RANK METRIC 97
6.1 DISTANCE MEASURES FOR CONVOLUTIONAL CODES IN RANK METRIC 97
6.1.1 DEFINITION OF DISTANCE PARAMETERS 98
6.1.2 UPPER BOUNDS ON DISTANCES OF (PARTIAL) UNIT MEMORY CODES 100
6.2 CONSTRUCTIONS OF CONVOLUTIONAL CODES IN RANK METRIC 101
6.2.1 PUM CODES BASED ON THE PARITY-CHECK MATRIX OF GABIDULIN CODES 101
6.2.2 PUM CODES BASED ON THE GENERATOR MATRIX OF GABIDULIN CODES 105
6.3 ERROR-ERASURE DECODING OF PUM GABIDULIN CODES 108
6.3.1 BOUNDED ROW DISTANCE CONDITION AND DECODING IDEA 108
6.3.2 PROOF OF CORRECTNESS OF THE ERROR-ERASURE DECODING ALGORITHM ILL
6.4 APPLICATION TO RANDOM LINEAR NETWORK CODING 114
6.4.1 MULTI-SHOT TRANSMISSION OF LIFTED PUM CODES 114
6.4.2 DECODING OF LIFTED PUM CODES IN THE OPERATOR CHANNEL 115
6.5 SUMMARY AND OUTLOOK
117
7 CONCLUDING REMARKS 119
A APPENDIX 121
A.L PROOFS FOR THE LINEARIZED EXTENDED EUCLIDEAN ALGORITHM 121
A.2 PROOF OF THE GENERALIZED TRANSFORMED KEY EQUATION 122
A.3 COMPARISON OF DECODING APPROACHES FOR GABIDULIN CODES 124
|
| any_adam_object | 1 |
| author | Wachter-Zeh, Antonia 1985- |
| author_GND | (DE-588)1044476966 |
| author_facet | Wachter-Zeh, Antonia 1985- |
| author_role | aut |
| author_sort | Wachter-Zeh, Antonia 1985- |
| author_variant | a w z awz |
| building | Verbundindex |
| bvnumber | BV041885251 |
| classification_rvk | ZN 6045 |
| ctrlnum | (OCoLC)915469679 (DE-599)DNB1047499665 |
| dewey-full | 005.72 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.72 |
| dewey-search | 005.72 |
| dewey-sort | 15.72 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Thesis Book |
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| indexdate | 2024-07-10T01:07:26Z |
| institution | BVB |
| isbn | 9783844026108 |
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| physical | XIV, 136 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Shaker |
| record_format | marc |
| series2 | Berichte aus der Informationstechnik |
| spelling | Wachter-Zeh, Antonia 1985- Verfasser (DE-588)1044476966 aut Decoding of block and convolutional codes in rank metric Antonia Wachter-Zeh Aachen Shaker 2014 XIV, 136 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Informationstechnik Zugl.: Ulm, Univ., Diss., 2013 Faltungscode (DE-588)4331752-2 gnd rswk-swf Decodierung (DE-588)4148976-7 gnd rswk-swf Blockcode (DE-588)4146024-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Blockcode (DE-588)4146024-8 s Faltungscode (DE-588)4331752-2 s Decodierung (DE-588)4148976-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027329292&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wachter-Zeh, Antonia 1985- Decoding of block and convolutional codes in rank metric Faltungscode (DE-588)4331752-2 gnd Decodierung (DE-588)4148976-7 gnd Blockcode (DE-588)4146024-8 gnd |
| subject_GND | (DE-588)4331752-2 (DE-588)4148976-7 (DE-588)4146024-8 (DE-588)4113937-9 |
| title | Decoding of block and convolutional codes in rank metric |
| title_auth | Decoding of block and convolutional codes in rank metric |
| title_exact_search | Decoding of block and convolutional codes in rank metric |
| title_full | Decoding of block and convolutional codes in rank metric Antonia Wachter-Zeh |
| title_fullStr | Decoding of block and convolutional codes in rank metric Antonia Wachter-Zeh |
| title_full_unstemmed | Decoding of block and convolutional codes in rank metric Antonia Wachter-Zeh |
| title_short | Decoding of block and convolutional codes in rank metric |
| title_sort | decoding of block and convolutional codes in rank metric |
| topic | Faltungscode (DE-588)4331752-2 gnd Decodierung (DE-588)4148976-7 gnd Blockcode (DE-588)4146024-8 gnd |
| topic_facet | Faltungscode Decodierung Blockcode Hochschulschrift |
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| work_keys_str_mv | AT wachterzehantonia decodingofblockandconvolutionalcodesinrankmetric |