Question: [10] (a) Show that E(x)=x is a prefix-code. (b) Consider a variant of the x code such that x = x1x2 ...xn is encoded as

[10]

(a) Show that E(x)=¯x is a prefix-code.

(b) Consider a variant of the ¯x code such that x = x1x2 ...xn is encoded as x11x21 ... 1xn−11xn0. Show that this is a prefix-code for the binary nonempty strings with l(¯x)=2l(x).

(c) Consider x = x1x2 ...xn encoded as x1x1x2x2 ... xn−1xn−1xn¬xn.

Show that this is a prefix-code for the nonempty binary strings.

(d) Give a prefix-code ˜x for the set of all binary strings x including , such that l(˜x)=2l(x) + 2.

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