[CC] Exercises

## 1.2

1.2.1: No, this is trivial.

1.2.2: f(n) = 2^n

1.2.3:

000000
000011
000101
000110
001001
001010
001100
001111
010001
010010
010100
010111
011000
011011
011101
011110
100001
100010
100100
100111
101000
101011
101101
101110
110000
110011
110101
110110
111001
111010
111100
111111

Aantal codewoorden: 2^5; als we 5 digits hebben dan volgt de zesde uit de eerdere vijf (is een "parity bit")

1.2.4:

A channel with p=0 can be turned into a channel with p=1 by always flipping the received bit.

1.2.5:
By flipping the received bit.

1.2.6: This channel is useless to us; its output is random.

## 1.3

1.3.4: If 001 is received, 001 is most likely the sent codeword.

1.3.5:
	a) yes; the number of digits is not even.
	b) 1100, 0101, 1001, 1111
	c) No. Each word of length 4 which does not belong to C has 4 different closest codewords.
	
1.3.6:
	a) 001001001
	b) 011011011
	c) 101101101
	d) 000000000

1.3.7: 2^{n-1}; this is the parity bit scheme

1.4.1:

For C = {all words of length 3}, the information rate is 1
For C' = C + parity digit, the information rate is 3/4
For C'' = C * 3, the information rate is 1/3

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