Introduction to coding and information theory:
This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variable-length codes that culminates in Kraft's Theorem. Two chapters on Information Theory follow - the first on Huffman encoding and the second on the concept of the entropy of an information source, culminating in a discussion of Shannon's Noiseless Coding Theorem. The remaining four chapters cover the theory of error-correcting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the sphere-packing, Singleton and Plotkin bounds, and a brief discussion of the Noisy Coding Theorem. There follows a chapter on linear codes that begins with a discussion of vector spaces over the field [actual symbol not reproducible]. The penultimate chapter is devoted to a study of the Hamming, Golay, and Reed-Muller families of codes, along with some decimal codes and some codes obtained from Latin squares. The final chapter contains a brief introduction to cyclic codes. |
| Beschreibung: | XIII, 323 S. graph. Darst. |
| ISBN: | 0387947043 |
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| 245 | 1 | 0 | |a Introduction to coding and information theory |c Steven Roman |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
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| 490 | 0 | |a Undergraduate texts in mathematics | |
| 520 | 3 | |a This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variable-length codes that culminates in Kraft's Theorem. Two chapters on Information Theory follow - the first on Huffman encoding and the second on the concept of the entropy of an information source, culminating in a discussion of Shannon's Noiseless Coding Theorem. The remaining four chapters cover the theory of error-correcting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the sphere-packing, Singleton and Plotkin bounds, and a brief discussion of the Noisy Coding Theorem. There follows a chapter on linear codes that begins with a discussion of vector spaces over the field [actual symbol not reproducible]. The penultimate chapter is devoted to a study of the Hamming, Golay, and Reed-Muller families of codes, along with some decimal codes and some codes obtained from Latin squares. The final chapter contains a brief introduction to cyclic codes. | |
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| 650 | 7 | |a Codes correcteurs d'erreurs (théorie de l'information) |2 ram | |
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Datensatz im Suchindex
| _version_ | 1804125716827078656 |
|---|---|
| adam_text | STEVE
N ROMA
N
INTRODUCTIO
N T
O
CODIN
G AN
D
INFORMATIO
N THEOR
Y
WIT
H 50 ILLUSTRATION
S
SPRINGER
CONTENT
S
PREFAC
E VI
I
INTRODUCTIO
N 1
0 PRELIMINARIE
S 5
0.1 MISCELLAN
Y 5
0.2 SOM
E PROBABILIT
Y 11
0.3 MATRICE
S 21
1 A
N INTRODUCTIO
N T
O CODE
S 2
5
1.1 STRING
S AN
D THING
S 25
1.2 WHA
T ARE CODES? 33
1.3 UNIQUEL
Y DECIPHERABL
E CODE
S 37
1.4 INSTANTANEOU
S CODE
S AN
D KRAFT S THEORE
M 42
1 INFORMATIO
N THEOR
Y 5
1
2 EFFICIEN
T ENCODIN
G 5
3
2.1 INFORMATIO
N SOURCES
; AVERAG
E CODEWOR
D LENGT
H ...
. 53
2.2 HUFFMA
N ENCODIN
G 57
XI
I
CONTENT
S
2.3 TH
E PROOF THA
T HUFFMA
N ENCODIN
G IS TH
E MOST EFFICIENT 63
3 NOISELES
S CODIN
G 6
9
3.1 ENTROP
Y 69
3.2 PROPERTIE
S OF ENTROP
Y 75
3.3 EXTENSION
S OF A
N INFORMATIO
N SOURC
E 79
3.4 TH
E NOISELES
S CODIN
G THEORE
M 82
I
I CODIN
G THEOR
Y 8
9
4 TH
E MAI
N CODIN
G THEOR
Y PROBLE
M 91
4.1 COMMUNICATION
S CHANNEL
S 91
4.2 DECISIO
N RULES 97
4.3 NEARES
T NEIGHBO
R DECODIN
G 103
4.4 TH
E MINIMU
M DISTANC
E OF A COD
E 106
4.5 PERFECT CODE
S AN
D TH
E SPHERE-PACKIN
G CONDITIO
N ...
. 116
4.6 MAKIN
G NE
W CODE
S FROM OLD CODE
S 124
4.7 TH
E MAI
N CODIN
G THEOR
Y PROBLE
M 131
4.8 SPHERE-COVERIN
G AN
D SPHERE-PACKIN
G BOUND
S 138
4.9 TH
E SINGLETO
N AN
D PLOTKI
N BOUND
S 142
4.10 INFORMATIO
N THEOR
Y REVISITED-
TH
E NOISY CODIN
G THEORE
M 146
5 LINEA
R CODE
S 14
9
5.1 TH
E VECTOR SPACE Z 149
5.2 LINEA
R CODE
S 163
5.3 CORRECTIN
G ERROR
S I
N A LINEA
R CODE 169
5.4 TH
E DUA
L OF A LINEA
R CODE 182
5.5 SYNDROM
E DECODIN
G 195
5.6 EQUIVALEN
T LINEA
R CODE
S 199
5.7 SOURC
E ENCODIN
G WIT
H A LINEA
R COD
E 208
6 SOM
E SPECIA
L CODE
S 21
7
6.1 TH
E HAMMIN
G AN
D GOLAY CODE
S 217
6.2 REED-MULLER CODE
S 234
6.3 SOM
E DECIMA
L CODE
S 245
6.4 CODE
S FROM LATI
N SQUARE
S 258
CONTENT
S
XIII
7 A
N INTRODUCTIO
N T
O CYCLI
C CODE
S 26
9
7.1 CYCLIC CODE
S 269
ANSWER
S T
O SELECTE
D ODD-NUMBERE
D EXERCISE
S 28
5
REFERENCE
S 31
7
INDE
X 31
9
|
| any_adam_object | 1 |
| author | Roman, Steven |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)34355037 (DE-599)BVBBV011218355 |
| dewey-full | 005.7/220 005.7/2 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.7/2 20 005.7/2 |
| dewey-search | 005.7/2 20 005.7/2 |
| dewey-sort | 15.7 12 220 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:05:59Z |
| institution | BVB |
| isbn | 0387947043 |
| language | German |
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| spelling | Roman, Steven Verfasser aut Introduction to coding and information theory Steven Roman New York [u.a.] Springer 1997 XIII, 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics This book is an introduction to coding and information theory, with an emphasis on coding theory. It is suitable for undergraduates with a modest mathematical background. While some previous knowledge of elementary linear algebra is helpful, it is not essential. All of the needed elementary discrete probability is developed in a preliminary chapter. After a preliminary chapter, there follows an introductory chapter on variable-length codes that culminates in Kraft's Theorem. Two chapters on Information Theory follow - the first on Huffman encoding and the second on the concept of the entropy of an information source, culminating in a discussion of Shannon's Noiseless Coding Theorem. The remaining four chapters cover the theory of error-correcting block codes. The first chapter covers communication channels, decision rules, nearest neighbor decoding, perfect codes, the main coding theory problem, the sphere-packing, Singleton and Plotkin bounds, and a brief discussion of the Noisy Coding Theorem. There follows a chapter on linear codes that begins with a discussion of vector spaces over the field [actual symbol not reproducible]. The penultimate chapter is devoted to a study of the Hamming, Golay, and Reed-Muller families of codes, along with some decimal codes and some codes obtained from Latin squares. The final chapter contains a brief introduction to cyclic codes. Codage ram Codes correcteurs d'erreurs (théorie de l'information) ram Information, Théorie de l' ram Coding theory Information theory Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s DE-604 Informationstheorie (DE-588)4026927-9 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007526264&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roman, Steven Introduction to coding and information theory Codage ram Codes correcteurs d'erreurs (théorie de l'information) ram Information, Théorie de l' ram Coding theory Information theory Codierungstheorie (DE-588)4139405-7 gnd Informationstheorie (DE-588)4026927-9 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4026927-9 |
| title | Introduction to coding and information theory |
| title_auth | Introduction to coding and information theory |
| title_exact_search | Introduction to coding and information theory |
| title_full | Introduction to coding and information theory Steven Roman |
| title_fullStr | Introduction to coding and information theory Steven Roman |
| title_full_unstemmed | Introduction to coding and information theory Steven Roman |
| title_short | Introduction to coding and information theory |
| title_sort | introduction to coding and information theory |
| topic | Codage ram Codes correcteurs d'erreurs (théorie de l'information) ram Information, Théorie de l' ram Coding theory Information theory Codierungstheorie (DE-588)4139405-7 gnd Informationstheorie (DE-588)4026927-9 gnd |
| topic_facet | Codage Codes correcteurs d'erreurs (théorie de l'information) Information, Théorie de l' Coding theory Information theory Codierungstheorie Informationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007526264&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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