A text is made up of the characters α, β, γ, δ and σ with the probability…
2014
A text is made up of the characters α, β, γ, δ and σ with the probability 0.12, 0.40, 0.15, 0.08 and 0.25 respectively. The optimal coding technique will have the average length of
Answer: B. 2.15 — Answer: 2.15 bits per symbol. Method (Huffman coding): combine the two smallest probabilities repeatedly. Combine δ (0.08) and α (0.12) → 0.20 Combine γ…
- A.
1.7
- B.
2.15
- C.
3.4
- D.
3.8
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Correct answer: B
Answer: 2.15 bits per symbol.
Method (Huffman coding): combine the two smallest probabilities repeatedly.
Combine δ (0.08) and α (0.12) → 0.20
Combine γ (0.15) and node 0.20 → 0.35
Combine σ (0.25) and node 0.35 → 0.60
Combine β (0.40) and node 0.60 → 1.00 (root)
Resulting codeword lengths (from the final tree):
β (0.40): length 1
σ (0.25): length 2
γ (0.15): length 3
α (0.12): length 4
δ (0.08): length 4
Compute the average length:
0.40 × 1 = 0.40
0.25 × 2 = 0.50
0.15 × 3 = 0.45
0.12 × 4 = 0.48
0.08 × 4 = 0.32
Total = 0.40 + 0.50 + 0.45 + 0.48 + 0.32 = 2.15
Therefore the optimal average code length is 2.15 bits per symbol.