(4) Given the following frequencies of letters appearing in a file, use Huffman Coding to determine the average number of bits used to encode a symbol, the binary code used to represent each bit, and the resulting binary tree. (20 pts.)
A: 0.08, B: 0.10, C: 0.12, D: 0.15, E: 0.20, F: 0.35
Huffmann Tree
Codewords: ----------- A - 000 B - 001 C - 100 D - 101 E - 01 F - 11
(4) Given the following frequencies of letters appearing in a file, use Huffman Coding to determine...
. Huffman Encoding (a.) (6 points) Suppose a certain file contains only the following letters with the corresponding frequencies 1 AİB 73 9 30 44 130 28 16 In a fixed-length encoding scheme, cach character is given a binary representation with the same number of bits. What is the minimum number of bits required to represent each letter of this file under fixed-length encoding scheme? Describe how to encode all seven letters in this file using the number of bits...
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more frequently can be encoded into strings of shorter lengths, while rarer letters can be turned into longer binary strings. On average, Huffman code is a more efficient way to encode a message as the number of bits in the output string will be shorter than if a fixed-length code was used....
4. Consider the given seven symbols with probabilities as {A, B, C, D, E, F, G} = {0.25, 0.20, 0.18, 0.15, 0.12, 0.06, 0.04}. Use Huffman coding to determine coding bits, entropy and average bits per symbol.
The following message is to be transmitted using Huffman coding: ISTHISHISTORYORISTHISHISTESTTHESIS a) Determine a Huffman code tree for this message. b) What are the corresponding code words for each character? c) What is the efficiency of this encoding compared to the uncompressed data? [Assume that the uncompressed characters are transmitted using the minimum number of bits needed to code all of the characters of the message.] d)What would be the decoded message if the following bit stream was sent using...
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
5. Eight letters {A, B, C, D, E, F,G,H} appear in a 100 letter length message with the following frequencies: 22, 6, 13, 19, 2, 9, 25, 4. (a) Use Huffman tree to design an optimal binary prefix code for the letters. (b) What is the average bit length of the message after apply codes designed in (a) to the message? [20 marks]
For this assignment, you will write a program to work with Huffman encoding. Huffman code is an optimal prefix code, which means no code is the prefix of another code. Most of the code is included. You will need to extend the code to complete three additional methods. In particular, code to actually build the Huffman tree is provided. It uses a data file containing the frequency of occurrence of characters. You will write the following three methods in the...
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities: A-0.10 C-0.17 E-0.21 B-0.21 D-0.06 F-0.25 (a) A: O, B: 10, C: 110, D: 1110, E: 11110, F: 11111 (b) A: 0,B: 10, C: 11111, D: 1110, E: 11110, F: 110 (c) A: 11110, B: 10, C: 1110, D: 11111, E: 110, F: 0 (d) A: 11111, B: 11110, C: 1110, D: 110, E: 10, F: 0 (e) A: 0,B: 01, C: 0001, D:...