From the encoding table as shown below: Table 1 Symbol Frequency Codeword A 0.29 0.25 100 0.13 101 D 0.15 1100 0.08 1101 0.07 1110 1111 G 0.03 a) Is this a valid prefix code? If yes, build the prefix tree according to the table above; if no, explain why not? b) Now, use Huffman code to assign new codewords to the symbols (A-G) above. Follow the convention that the group/symbol with higher probability is assigned a *0' and that with lower probability is assigned a 1'. List out all the codewords. Frequency Codeword (Huffman) Symbol A 0.29 B 0.25 0.13 D 0.15 0.08 0.07 0.03 c) What is the average codeword length of the original coding (Table 1)? d) What is the average codeword length using Huffman code in part b)? e) What is the minimum average number of bits needed to encode each symbol? f) Using a fixed-length code, what will be the minimum average number of bits needed to encode each symbol?