1. [14] From the encoding table as shown below: Table 1 Symbol Frequency Codeword A B C D E F G 0.29 0.25 0.13 0.15 0.08 0.07 0.03 ABCDEFG 0 100 101 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. 1100 1101 1110 1111 Symbol Frequency Codeword (Huffman) 0.29 0.25 0.13 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 bi need to encode each symbol? f) Using a fixed-length code, what will be the minimum average number of bits needed to encode each symbol?