Coding and Information Theory

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Springer Science & Business Media, Jun 4, 1992 - Mathematics - 488 pages
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This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra.
 

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Contents

IV
11
V
12
VI
16
VII
18
VIII
22
IX
23
XII
26
XIII
28
CXLII
260
CXLIII
262
CXLV
263
CXLVII
267
CXLIX
268
CL
269
CLI
270
CLII
272

XIV
30
XVI
33
XVII
39
XVIII
40
XIX
41
XXI
43
XXII
44
XXIII
47
XXIV
52
XXVI
54
XXVII
56
XXVIII
59
XXIX
62
XXX
64
XXXI
69
XXXII
72
XXXIII
76
XXXIV
81
XXXV
83
XXXVI
84
XXXVII
89
XXXVIII
91
XXXIX
92
XL
93
XLI
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XLII
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XLIII
98
XLIV
101
XLV
105
XLVI
106
XLVII
107
XLVIII
111
XLIX
117
L
119
LI
122
LIII
123
LV
126
LVI
129
LVII
131
LVIII
132
LIX
134
LX
136
LXI
138
LXII
143
LXIII
144
LXIV
145
LXVI
149
LXVII
150
LXX
151
LXXII
152
LXXIV
153
LXXV
154
LXXVIII
155
LXXX
156
LXXXII
157
LXXXIII
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LXXXV
159
LXXXVI
163
LXXXVIII
165
LXXXIX
167
XC
170
XCII
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XCIV
172
XCV
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XCVII
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XCIX
175
C
176
CI
178
CII
181
CIII
183
CIV
188
CV
197
CVI
199
CVII
202
CVIII
205
CIX
206
CXI
208
CXII
210
CXIII
212
CXIV
216
CXVI
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CXVII
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CXVIII
220
CXIX
222
CXX
223
CXXI
225
CXXII
226
CXXIII
228
CXXIV
230
CXXV
235
CXXVIII
237
CXXIX
239
CXXX
240
CXXXI
245
CXXXII
246
CXXXIII
250
CXXXIV
251
CXXXV
253
CXXXVI
254
CXXXVII
256
CXL
258
CLIII
274
CLIV
275
CLV
276
CLVI
278
CLVII
285
CLVIII
286
CLIX
287
CLX
288
CLXI
289
CLXII
296
CLXIII
297
CLXIV
299
CLXV
300
CLXVI
301
CLXVII
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CLXVIII
304
CLXIX
308
CLXXI
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CLXXII
310
CLXXIII
312
CLXXIV
314
CLXXV
315
CLXXVI
320
CLXXVII
321
CLXXVIII
325
CLXXIX
327
CLXXX
328
CLXXXI
331
CLXXXII
333
CLXXXIII
335
CLXXXIV
336
CLXXXV
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CLXXXVII
344
CXC
345
CXCI
347
CXCII
349
CXCIV
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CXCV
354
CXCVI
356
CXCVII
358
CXCVIII
360
CXCIX
362
CCI
363
CCV
365
CCVI
369
CCVIII
370
CCIX
371
CCX
372
CCXI
374
CCXII
375
CCXIII
376
CCXIV
377
CCXV
379
CCXVII
380
CCXVIII
381
CCXIX
382
CCXX
386
CCXXII
389
CCXXIII
390
CCXXIV
393
CCXXV
395
CCXXVI
396
CCXXVII
398
CCXXVIII
401
CCXXIX
407
CCXXXI
409
CCXXXII
412
CCXXXIV
414
CCXXXV
417
CCXXXVII
421
CCXXXVIII
422
CCXXXIX
423
CCXL
425
CCXLII
426
CCXLIV
427
CCXLV
428
CCXLVI
429
CCXLVIII
430
CCLII
431
CCLIV
432
CCLV
433
CCLVII
435
CCLIX
436
CCLX
440
CCLXI
441
CCLXII
442
CCLXIII
443
CCLXIV
445
CCLXV
446
CCLXVI
449
CCLXVIII
452
CCLXIX
456
CCLXX
459
CCLXXI
463
CCLXXII
464
CCLXXIII
468
CCLXXIV
469
CCLXXV
475
CCLXXVI
479
CCLXXVII
481
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