Question: [26] (a) Show that the set of code words {x : x N} is a universal code-word alphabet. Show that it is not asymptotically optimal.

[26]

(a) Show that the set of code words {x¯ : x ∈N} is a universal code-word alphabet. Show that it is not asymptotically optimal.

(b) Show that the set of code words {l(x)x : x ∈ N} is a universal code-word alphabet. Show that it is also asymptotically optimal.

Comments. Source: [P. Elias, IEEE Trans. Inform. Theory, IT-21(1975), 194–203].

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