Index
a-separated, 103, 187
absolutely regular, 179, 233
addition law, 58
admissible, 174
in probability, 174
in J, 184
almost block-independence (ABI), 212
almost blowing-up (ABUP), 195, 235
alphabet, 1
asymptotic equipartition (AEP), 55
B-process, 8, 211
Barron's code-length bound, 125
base (bottom) of a column, 107
of a column structure, 108
binary entropy function, 52
block code, 8
block coding of a process, 8
block-independent process, 211
block-structure measure, 104
block-to-stationary construction, 83
blowing-up property (BUP), 194
almost blowing-up, 195, 235
(8, O-blowing-up, 195, 235
blowup, 68
blowup bound, 68
5-blowup, 185, 194
Borel-Cantelli principle, 11
building blocks, 69
built by cutting and stacking, 109
built-up, 69
built-up set bound, 70
(1 - O-built-up, 138
circular fc-type, 123
code, 71
code sequence, 74, 121
rate of, 74
codebook, 72
codeword, 71
coding block, 84, 215
faithful (noiseless), 71
length function, 72, 121
n-code, 121
per-symbol, 7
truncation, 215
column, 24, 107
base (bottom), 24, 107
cutting a column, 109
disjoint columns, 107
height (length), 24, 107
labeling, 107
level, 24, 107
name, 107
subcolumn, 108
support, 107
top, 24, 107
upward map, 108
width (thickness), 24, 104, 107
column partitioning, 109
column structure, 107
complete sequences, 110
transformation defined by, 110
copy, 115
cutting into copies, 115
disjoint column structures, 108
estimation of distributions, 111
column structure:
top, 108
uniform, 188
upward map, 108
width, 108
width distribution, 108
(a, £)-separated structures, 189
(a, #)-strongly-separated, 190
columnar representation, 105
complete sequences of structures, 110
concatenated-block process, 9, 10
concatenation representation, 26, 27
conditional ^-independence, 226
entropy, 58
245
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