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Hamming R.W. — Coding and Information Theory
Hamming R.W. — Coding and Information Theory

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Название: Coding and Information Theory

Автор: Hamming R.W.

Аннотация:

The second edition is mainly an expansion of the material in the first edition. The changes were made to (1) increase the clarity of the presentation, (2) extend some of the basic ideas, and (3) indicate further practical details. 1 have resisted the urgings (both from others and myself) to include more difficult codes, such as Reed-Muller, Vitcrbi, Fire, and cyclic. They seem to be more suitable for a second course, and in any case require a firmer mathematical background than 1 have assumed, if they are to be "understood." I still believe that it is better, in this subject, to master the fundamentals than it is to rush through, with little real understanding, a large body of material. There are now many excellent texts devoted to algebraic coding theory.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1986

Количество страниц: 259

Добавлена в каталог: 23.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abramson, N.      253
Abstract theory      1
Adjoint system      133
Algebraic coding theory      209
AM signaling      242
AND      30
Anti-Gray code      99
ASCII code      8 10 11 27
ASCII code, table of      13
Average code length      2 63
Average error probability      201
Average random code      201
Backward conditional probabilities      142
Bandwidth      237
Bandwidth example      238
Bandwidth generally      246
Bandwidth vs. change      242
Bayes' formula (theorem)      141
Berlekamp, E.R.      253
Bernoulli trials      183
Binary encoding      7
Binary symmetric channel      18 142 159 195
Binary symmetric channel, capacity of      160—161
Binomial coefficient bound      170—173
Binomial coefficients      13
Bit      7
Bit of information      106
Blake, I.      253
Block code      68
Burst error—detecting codes      26
BYTE      10
Cain, F.B.      253
Carrier frequency      224
Cauchy functional equation      104
Channel      138
Channel capacity      103 201
Channel capacity of binary symmetric channel      160—161
Channel capacity, definition of      153
Channel capacity, encoding      5
Channel relationships      140
Channel uniform      154—155
Channel, definition of      139
Channel, encoding      2
Channel, properties of      140
Chebyshev's inequality      181—182
Clark, G.      253
Code compression      18
Codes 2-out-of-5      14 23
Codes anti-Gray      99
Codes comma      54 59 69
Codes delta modulation      100
Codes Gray      80 97
Codes hash      94
Codes Huffman      51
Codes instantaneous      53—55
Codes miscellaneous      79
Codes Morse      12—13
Codes radix r      15
Codes random      79
Codes Shannon — Fano      121—122 126
Codes van Duuren (3-out-of-7)      23
Codes variable—length      12 51
Codes, burst—detecting      26
Codes, error—correcting      34
Codes, error—detecting      20
Codes, extensions of      72
Codes, hexadecimal      10
Codes, octal      9
Codes, predictive      79
Codes, resynchronization of      101
Codes, unique      52
Codes, weighted      27
Coding Huffman      51
Coding Shannon — Fano      121
Combinations      13
Comma codes      54 69
Conditional mutual information      150 161
Conditional probability      80
Continuous signals      247
Costello, D.J.      254
Davidson, L.D.      253
Decision rule      192
Decision tree      53
Decoding tree      54 56—57 60 62
Delta modulation      100
Digital signaling      6 237
Direct product      53
Double-error-correcting code      228—234
Double-error-detecting code      47
Efficient codes      51 56 64
Efficient codes Markov      86
Eigenfunctions      237
England, J.      254
entropy      103 107
Entropy function      1 107
Entropy function fundamental inequality      115
Entropy function, maximum of      117
Entropy function, properties of      114—119
Entropy function, table of      250
Entropy joint      146
Entropy of Markov processes      129
Entropy of source      18
Entropy received symbols      145
Entropy robustness      136
Entropy source alphabet      145
Entropy, conditional      130 146
Equilibrium probabilities      133
Equivalent codes      42
Equivocation      148
Ergodic Markov processes      85
Error correction      34
Error integral      174
Error-correcting codes      35—36 158
Error-correcting codes, perfect      158
Errors of interchange of symbols      28
Error—detecting codes      20 22 147 210
Error—detecting codes probability      24
Error—detecting codes why      20
escape characters      15
Evolution      3
Excess redundancy      22
Extensions of a code      53 72 124
Extensions of a code examples      126
Extensions of a code Markov process      87
Fano bound      205
Finite automation      53 77
Finite fields      210
FM signaling      244
FORTRAN      16 49 95
FORTRAN, compile      17
Forward conditional probabilities      141
Fourier integral      238
Fundamental error formula      199
Gallager, R.G.      253
Galois fields      4 195
Gamma function      173
Gatlin, L.L.      253
Geometric approach      44
Gibbs inequality      117
Gray codes      80 97
Gray codes, decoding      99
Gray codes, details of      98
Gray, R.M.      253
Gray, R.M. code      97
Guiasu, S.      254
Hamming error-correcting codes      210—211 213 220
Hamming error-correcting codes example      41
Hamming error-correcting codes parity checks      39 210
Hamming error-correcting codes, table of      40
Hamming — Huffman coding      78
Hamming, distance      45 189
Hamming, meaning of      46
Hartley      106
Hash coding      94
Hash coding collisions      95
Hash coding removals      96
Hexadecimal code      10
history      2
Huffman codes      51 63 71 114
Huffman codes, examples of      65 67—68
Huffman codes, noise in      74
Huffman codes, radix r      73
Huffman codes, use of      77
Huffman codes, variability of      68
Independent errors      23
Information source      1 5
Information source, definition of      104
Instantaneous codes      53
Instantaneous codes, construction of      55
Interchange of symbols      28
ISBN book numbers      32
Jacobs, I.M.      254
Jayant, N.S.      254
Knuth, D.E.      254
Kraft inequality      57 62 121
Kraft inequality theorem      57
Law of Large Numbers      183
Law of large numbers theorem      184
Lin, S.      254
Logical add (XOR)      23 31
MacWilliams, J.      254
Markov process      80 129 131 135
Markov process, ergodic      84
Martin, N.      254
Maximum likelihood rule      192 196
McEliece, R.J.      254
McMillan inequality      62
Memory source      80
Metalanguage      16
Midpoint formula      166
Minimum distance      45
Minimum variance codes      68 75
Model of signaling system      4
Modular arithmetic      30
Modulation      242
Modulo 2 arithmetic      21
Monic polynomial      215
Morse code      12 13 51 63
Morse code, table of      13
Mutual information      148
Mutual information, definition of      148
Mutual information, properties of      149—151
nat (unit of information)      106
Noise      23
Noise entropy      148
Noise in Huffman codes      74
Noise power      248
Noiseless coding theorem      104 125
NORC computer      34
n—dimensional codes      37 45
n—dimensional paradox      179
n—dimensional space      176
n—dimensional space Euclidean distance      176
n—dimensional space, Euclidean      176
n—dimensional spheres      177
n—dimensional spheres coefficients      177
n—dimensional spheres, formula for      177
n—dimensional spheres, table of      177
Octal code      9
Omura, J.K.      254
Parity check      21 40
Parity check even      21
Parity check odd      21
Parity check, computing      22
Peterson, W.W.      254
Pless, V.      254
Polynomials      214
Polynomials primitive root      219
Polynomials, prime      215
Predictive encoding      79 88
Predictive encoding decoder      90
Predictive encoding encoder      89
Predictive encoding run length      91
Predictive encoding summary      94
Prime polynomials      215
Primitive roots      219
Probabilities of symbols      1 63
Pulse signaling      245
Radix r codes      15 72
Random code      196 203
Random code, average of      201
Random encoding      79 196
Random type fonts      118
Rectangular codes      35
Redundancy      22 36
reliable      20
Restrictions on codes      21
Resynchronization      101
Retransmission      25
Sampling theorem      240
Shannon      2
Shannon's theorems, main      191
Shannon's theorems, main converse      207
Shannon's theorems, main general case of      204
Shannon's theorems, noiseless      125
Shift registers      224
Shortened block codes      60
Side lobes      240
Single-error-detecting plus double-error-correcting codes      46 228
Slepian, D.      254
Sloane, N.J.A.      254
Source alphabet      2 6
Source encoding      2 5
Stirling's approximation      165—170
Stirling's approximation, table of      170
Stretch computer      35
Symbol      1
Symmetric channel      18
Syndrome      38 39 212
Thompson, T.M.      254
Transition graph      81
Transition graph equilibrium      83
Transition graph limiting matrix      83
Transition graph matrix      82
Transition graph probability      82
Trapezoid Rule      165
Triangular codes      37
Two state devices      6
Two-out-of-five codes      14 23
Two-out-of-five codes table      14
Uniform channel      154—155
Uniform channel definition      155
Uniform input      156
Unique decoding      52 62
van Duuren code (3 out of 7)      23
Variable length codes      13 51
Variance      181
Variance minimum      75
Variance of sums      184
Viterbi, A.J.      254
Wakerly, J.      254
Wallis integrals      168
Weighted codes      27
Weldon, E.J., Jr.      254
White noise      23 39
Wozencraft, J.M.      254
XOR (instruction)      30
Zipf distribution      71
Zipf distribution, entropy of      112
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