Suppose an alphabet consists of 6 symbols, and the probability for each of the symbols is $1 / 6$. (Note, $\log _{2}(3)=1.585$ )
(a) What is the entropy for this set?
(b) Draw the Shannon-Fano tree for this set. What is the average bitrate?
(c) Draw the Huffman tree for this set. What is the average bitrate?
(d) How many bits would we need without compression, assuming fixed-length codewords? What is the compression ratio, compared to the Huffman tree?

Question

Suppose an alphabet consists of 6 symbols, and the probability for each of the symbols is $1 / 6$. (Note, $\log _{2}(3)=1.585$ ) 
(a) What is the entropy for this set?
(b) Draw the Shannon-Fano tree for this set. What is the average bitrate?
(c) Draw the Huffman tree for this set. What is the average bitrate?
(d) How many bits would we need without compression, assuming fixed-length codewords? What is the compression ratio, compared to the Huffman tree?

Quizplus · Accepted Answer

The Answer of Suppose an alphabet consists of 6 symbols, and the probability for each of the symbols is $1 / 6$. (Note, $\log _{2}(3)=1.585$ ) 
(a) What is the entropy for this set?
(b) Draw the Shannon-Fano tree for this set. What is the average bitrate?
(c) Draw the Huffman tree for this set. What is the average bitrate?
(d) How many bits would we need without compression, assuming fixed-length codewords? What is the compression ratio, compared to the Huffman tree?

Suppose an Alphabet Consists of 6 Symbols, and the Probability 1/61 / 61/6

Suppose an Alphabet Consists of 6 Symbols, and the Probability $1 / 6$