Question: [22] Let a code have the set of code-word lengths l1, l2,... . Show that if the code is uniquely decodable, then the Kraft inequality,

[22] Let a code have the set of code-word lengths l1, l2,... .

Show that if the code is uniquely decodable, then the Kraft inequality, Theorem 1.11.1, must be satisfied.

Comments. Thus, Theorem 1.11.1 holds for the wider class of uniquely decodable codes. This is called the McMillan–Kraft Theorem. Source:

[R.G. Gallager, Information Theory and Reliable Communication, Wiley, 1968]. Attributed to B. McMillan.

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