Construct a Binary Huffman Code for a Source$S$ With Three Symbols

Question

Examlex · Accepted Answer

The Answer is (a) A: 1; B: 00; C: 01;
Average

=0.1 * 2+0.3 * 2+0.6 * 1=1.4

bits/symbol
Entropy

=-

sum

p_{i} \log p_{i}=\mathbf{1 . 2 9 5 5}

(b) Tree is per Fig. 7.1.
Codeword bitlengths are:
$(a) A: 1; B: 00; C: 01; Average =0.1 * 2+0.3 * 2+0.6 * 1=1.4 bits/symbol Entropy =- sum p_{i} \log p_{i}=\mathbf{1 . 2 9 5 5} (b) Tree is per Fig. 7.1. Codeword bitlengths are: Average =0.5 *(0.36+3 imes 0.18+3 imes 0.18+4 imes 0.09+4 imes 0.06+4 imes 0.06+5 imes 0.03+6 imes 0.03+6 imes 0.01) =1.3350 The best possible is the entropy, given by: H=-0.1 \lg (0.1)+-0.3 \lg (0.3)-0.6 \lg (0.6)=1.2954618$ Average

=0.5 *(0.36+3 imes 0.18+3 imes 0.18+4 imes 0.09+4 imes 0.06+4 imes 0.06+5 imes 0.03+6 imes 0.03+6 imes 0.01)

=1.3350

The best possible is the entropy, given by:

H=-0.1 \lg (0.1)+-0.3 \lg (0.3)-0.6 \lg (0.6)=1.2954618

Construct a Binary Huffman Code for a Source $S$ With Three Symbols

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Construct a Binary Huffman Code for a Source SSS With Three Symbols

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Correct Answer:VerifiedShow Answer

Construct a Binary Huffman Code for a Source $S$ With Three Symbols

Correct Answer:
Verified