December 2002
Intermediate to advanced
454 pages
25h 39m
English
Content preview from Lossless Compression Handbook
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16 PART I / THEORY
Kraft's inequality and its counterpart play an important role in the analysis and design of codes
for (memoryless) sources as we will see in the following sections.
1.3.4 Redundancy, Entropy, and Bounds
Remember that we are still discussing variable-length codes for symbols generated by memoryless
sources. The source distribution is {p(x) 9 x e X} and a code is described by {c(x) 9 x e X}.
Definition 1.6. We define the individual redundancy p(x) of the symbol x ~ X, whose co&word
c(x) has length l (x) as
1
p(x) ~- 1 (x) - log 2 p(x )' ( 1.31 )
and the expected redundancy of a code as
ED(X)] ~ ~
p(x)p(x).
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